Olav Kristian Gunnarson Dovland

Professor Department of Mathematical Sciences

Email: olav.dovland@uia.no
Phone: +47 38 14 15 42
Mobile phone: +47 92 02 16 86
Office: J3050 (Universitetsveien 25, 4630 Kristiansand, Norway)

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Areas of responsibility

Master degree in applied mathematics, University of Bergen, 1991. Pedagogical seminar 1992. Doctoral degree in pure mathematics, University of Bergen, 2001.

Research

Academic interests

My research field is Geometry of Banach spaces. I have been teaching most of basic mathematical subjects.

Research groups

Functional Analysis

Dovland, Olav Kristian; Põldvere, Märt; Troyanski, Stanimir & Viil, Tauri (2024). Strictly convex renormings and the diameter 2 property. Studia Mathematica. ISSN 0039-3223. 274(1), p. 37–49. doi: 10.4064/sm221216-28-8. Full text in Research Archive Show summary
A Banach space (or its norm) is said to have the diameter 2 property (D2P in short) if every nonempty relatively weakly open subset of its closed unit ball has diameter 2. We construct an equivalent norm on L_1[0,1] which is weakly midpoint locally uniformly rotund and has the D2P. We also prove that for Banach spaces admitting a norm-one finite-co-dimensional projection it is impossible to be uniformly rotund in every direction and at the same time have the D2P.
Dovland, Olav & Rodriguez, Jose (2022). Isometric factorization of vector measures and applications to spaces of integrable functions. Journal of Mathematical Analysis and Applications. ISSN 0022-247X. 508(1). doi: 10.1016/j.jmaa.2021.125857. Full text in Research Archive Show summary
Let X be a Banach space, Σ be a σ-algebra, and be a (countably additive) vector measure. It is a well known consequence of the Davis-Figiel-Johnson-Pełczyński factorization procedure that there exist a reflexive Banach space Y, a vector measure and an injective operator such that m factors as . We elaborate some theory of factoring vector measures and their integration operators with the help of the isometric version of the Davis-Figiel-Johnson-Pełczyński factorization procedure. Along this way, we sharpen a result of Okada and Ricker that if the integration operator on is weakly compact, then is equal, up to equivalence of norms, to some where Y is reflexive; here we prove that the above equality can be taken to be isometric.
Abrahamsen, Trond Arnold; Dovland, Olav & Poldvere, Mert (2019). New applications of extremely regular function spaces. Pacific Journal of Mathematics. ISSN 0030-8730. 301(2). doi: 10.2140/pjm.2019.301.385. Full text in Research Archive Show summary
Let L be an infinite locally compact Hausdorff topological space. We show that extremely regular subspaces of C0(L) have very strong diameter 2 properties and, for every real number ε with 0 <ε<1, contain an ε-isometric copy of c0. If L does not contain isolated points they even have the Daugavet property, and thus contain an asymptotically isometric copy of ℓ1.
Abrahamsen, Trond Arnold; Dovland, Olav Kristian & Põldvere, Märt (2019). New applications of extremely regular function spaces. Pacific Journal of Mathematics. ISSN 0030-8730. 301(2), p. 385–394. doi: 10.2140/pjm.2019.301.385. Full text in Research Archive
Abrahamsen, Trond Arnold; Hájek, Petr; Nygaard, Olav Kristian & Troyanski, Stanimir (2018). Strongly Extreme Points and Approximation Properties. Canadian Mathematical Bulletin (CMB). ISSN 0008-4395. 61(3), p. 449–457. doi: 10.4153/CMB-2017-067-3. Full text in Research Archive
Abrahamsen, Trond Arnold; Martiny, Andre; Leraand, Aleksander & Nygaard, Olav Kristian (2017). Two properties of Müntz spaces. Demonstratio Matematicae. ISSN 0420-1213. 50(1), p. 239–244. doi: 10.1515/dema-2017-0025. Full text in Research Archive Show summary
We show that Müntz spaces, as subspaces of C[0, 1], contain asymptotically isometric copies of c0 and that their dual spaces are octahedral.
Lima, Vegard; Abrahamsen, Trond Arnold; Nygaard, Olav Kristian & Troyanski, Stanimir (2016). Diameter two properties, convexity and smoothness. Milan Journal of Mathematics. ISSN 1424-9286. 84(2), p. 231–242. doi: 10.1007/s00032-016-0258-1. Full text in Research Archive
Abrahamsen, Trond Arnold; Hájek, Petr; Nygaard, Olav Kristian; Talponen, Jarno & Troyanski, Stanimir (2016). Diameter 2 properties and convexity. Studia Mathematica. ISSN 0039-3223. 232(3), p. 227–242. doi: 10.4064/sm8317-4-2016. Full text in Research Archive
Abrahamsen, Trond Arnold; Langemets, Johann; Lima, Vegard & Nygaard, Olav Kristian (2015). On thickness and thinness of Banach spaces. Houston Journal of Mathematics. ISSN 0362-1588. 41(1), p. 97–111. Full text in Research Archive
Abrahamsen, Trond Arnold; Lima, Vegard & Nygaard, Olav Kristian (2014). Almost isometric ideals in Banach spaces. Glasgow Mathematical Journal. ISSN 0017-0895. 56(2), p. 395–407. doi: 10.1017/S0017089513000335. Full text in Research Archive
Abrahamsen, Trond Arnold; Lima, Vegard & Dovland, Olav (2013). Remarks on diameter 2 properties. Journal of Convex Analysis. ISSN 0944-6532. Full text in Research Archive
Abrahamsen, Trond Arnold; Lima, Vegard & Nygaard, Olav Kristian (2013). Remarks on Diameter 2 properties. Journal of Convex Analysis. ISSN 0944-6532. 20(2), p. 439–452. Full text in Research Archive Show summary
If X is an infinite-dimensional uniform algebra, if X has the Daugavet property or if X is a proper M-embedded space, every relatively weakly open subset of the unit ball of the Banach space X is known to have diameter 2, i.e., X has the diameter 2 property. We prove that in these three cases even every finite convex combination of relatively weakly open subsets of the unit ball have diameter 2. Further, we identify new examples of spaces with the diameter 2 property outside the formerly known cases; in particular we observe that forming lp-sums of diameter 2 spaces does not ruin diameter 2 structure.
Abrahamsen, Trond Arnold & Nygaard, Olav (2011). On λ-strict ideals in banach spaces. Bulletin of the Australian Mathematical Society. ISSN 0004-9727. 83(2), p. 231–240. doi: 10.1017/S0004972710001735. Full text in Research Archive
Gebremichael, Andualem Tami; Goodchild, Simon & Nygaard, Olav (2011). STUDENTS PERCEPTIONS ABOUT THE RELEVANCE OF MATHEMATICS IN AN ETHIOPIAN PREPARATORY SCHOOL. In Pytlak, Marta; Rowland, Tim & Swoboda, Ewa (Ed.), CERME 7: Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education. European Society for Research in Mathematics Education. ISSN 9788373386839. p. 1430–1439. Full text in Research Archive Show summary
This paper presents results from a pilot study into students’ perceptions of the relevance of mathematics. Cultural historical activity theory is used as an analytical perspective. Data are collected through interviews supported by classroom observation. Convenience and purposive sampling were used to select the school and students. Findings indicate that students perceive that only basic mathematics is used in their everyday activities whereas the mathematics they are learning at the moment: has an indirect relevance through other subjects or used by professionals; has use in their future studies; has an exchange value in the market place of joining the university and getting job; and in mathematics they experience a sense of identity, empowerment, spirituality, and trust in the curriculum and their teacher.
Viitala, Hanna Leena; Grevholm, Barbro & Nygaard, Olav (2011). About affect in five Finnish dissertations on mathematical thinking. In Kislenko, Kirsti (Eds.), Current state of research on mathematical beliefs XVI, Proceedings of the MAVI-16 Conference, June 26-29, 2010, Tallinn, Estonia. Tallin University. ISSN 9789949463794. p. 313–330. Full text in Research Archive
Abrahamsen, Trond Arnold & Nygaard, Olav (2011). ON lambda-STRICT IDEALS IN BANACH SPACES. Bulletin of the Australian Mathematical Society. ISSN 0004-9727. 83(2), p. 231–240. doi: 10.1017/S0004972710001735. Full text in Research Archive
Nygaard, Olav Kristian & Poldvere, Mert (2009). Johnson's projection, Kalton's property (M*), and M-ideals of compact operators. Studia Mathematica. ISSN 0039-3223. 195(3), p. 243–255. doi: 10.4064/sm195-3-4. Full text in Research Archive Show summary
Let X and Y be Banach spaces. We give a \non-separable" proof of theKalton{Werner{Lima{Oja theorem that the subspace K(X;X) of compact operators formsan M-ideal in the space L(X;X) of all continuous linear operators from X to X if andonly if X has Kalton's property (M_) and the metric compact approximation property.Our proof is a quick consequence of two main results. First, we describe how Johnson'sprojection P on L(X; Y )_ applies to f 2 L(X; Y )_ when f is represented via a Borel(with respect to the relative weak_ topology) measure on BX__ BY _w__ L(X; Y )_: IfY _ has the Radon{Nikod_ym property, then P \passes under the integral sign". Our basictheorem en route to this description|a structure theorem for Borel probability measureson BX__ BY _w_|also yields a description of K(X; Y )_ due to Feder and Saphar. Second,we show that property (M_) for X is equivalent to every functional in BX__ BX_w_behaving as if K(X;X) were an M-ideal in L(X;X).
Nygaard, Olav Kristian & Poldvere, Mert (2009). RESTRICTED UNIFORM BOUNDEDNESS IN BANACH SPACES. Quaestiones Mathematicae. Journal of the South African Mathematical Society. ISSN 1607-3606. 32(1), p. 5–14. doi: 10.2989/QM.2009.32.1.2.704. Full text in Research Archive Show summary
Precise conditions for a subset A of a Banach space X are known in order that pointwise bounded on A sequences of bounded linear functionals on X are uniformly bounded. In this paper, we study such conditions under the extra assumption that the functionals belong to a given linear subspace G of X*. When Gamma = X*, these conditions are known to be the same ones assuring a bounded linear operator into X, having A in its image, to be onto. We prove that, for A, deciding uniform boundedness of sequences in G is the same property as deciding surjectivity for certain classes of operators.
Nygaard, Olav Kristian & Poldvere, Mert (2007). Families of vector measures of uniformly bounded variation. Archiv der Mathematik. ISSN 0003-889X. 88. Full text in Research Archive Show summary
We characterize families of vector measures of uniformly bounded variation and semivariation in terms of additivity properties. A classical theorem of Rickart and a simplified proof of Nikod m's boundedness theorem follow.
Nygaard, Olav Kristian; Abrahamsen, Trond Arnold & Poldvere, Mert (2006). On weak integrability and boundedness in Banach spaces. Journal of Mathematical Analysis and Applications. ISSN 0022-247X. 314, p. 67–74. Full text in Research Archive Show summary
Thin and thick sets in normed spaces were defined and studied by M.I. Kadets and V.P. Fonf in 1983. In this paper, we give a new characterization of thick sets in terms of weak integrability of Banach space valued measurable functions. We also characterize thick sets in terms of boundedness of vector measures, and explain how this concept is related to the theory of barrelled spaces.
Zernichow, Anja Glad & Nygaard, Olav Kristian (2006). Den blokkerende misoppfatning. Spesialpedagogikk. ISSN 0332-8457. 71(4), p. 34–38. Full text in Research Archive
Nygaard, Olav Kristian (2006). Thick sets in Banach spaces and their properties. Questiones Mathematicae. ISSN 0379-9468. 29(1), p. 59–72. Full text in Research Archive Show summary
We make a survey over results involving the concepts thick and w*-thick set and provide a lot of known such sets. We show that the long standing 'separable quotient problem' and a problem from function theory is closely connected to thickness.
Nygaard, Olav Kristian & Tollevik, Siv Anne (2005). Når det blir vanskelig ... en tankevekker om fjernstudentens situasjon, Norgesuniversitetets skriftserie. Norgesuniversitetet. p. 11–22. Full text in Research Archive
Nygaard, Olav Kristian (2005). A remark on Rainwater's theorem. Annales Mathematicae et Informaticae. ISSN 1216-6014. 32, p. 125–127. Full text in Research Archive Show summary
We define Rainwater sets as subsets of the dual of a Banach space for which Rainwater's theorem holds and show that (I)-generating subsets have this property. We apply this observation to give a proof of James' theorem when the dual unit ball is sequentially compact in its weak-star topology.
Lima, Åsvald; Lima, Vegard & Nygaard, Olav Kristian (2004). On the compact approximation property. Studia Mathematica. ISSN 0039-3223. 160(2), p. 185–200. Full text in Research Archive
Nygaard, Olav Kristian (2002). Boundedness and surjectivity in normed spaces. International Journal of Mathematics and Mathematical Sciences. ISSN 0161-1712. 32, p. 149–165. Full text in Research Archive
Nygaard, Olav Kristian (2001). Some dual Tauberian embeddings. Acta et Commentationes Universitatis Tartuensis de Mathematica. ISSN 1406-2283. 5, p. 35–41. Full text in Research Archive
Nygaard, Olav Kristian & Werner, Dirk (2001). Slices in the unit ball of a uniform algebra. Archiv der Mathematik. ISSN 0003-889X. 76, p. 441–444. Full text in Research Archive Show summary
We show that every nonvoid relatively weakly open subset, in paricular every slice, of the unit ball of a uniform algebra has diameter 2.
Nygaard, Olav Kristian (2001). A strong Uniform boundedness principle in Banach spaces. Proceedings of the American Mathematical Society. ISSN 0002-9939. 129(3), p. 861–863. Full text in Research Archive
Lima, Åsvald; Nygaard, Olav & Oja, Eve (2000). Isometric factorization of weakly compact operators and the approximation property. Israel Journal of Mathematics. ISSN 0021-2172. 119, p. 325–348. Full text in Research Archive

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Dovland, Olav & Pettersen, Petter (2019). Matematikk for økonomistudenter, 3. utg. Fagbokforlaget. ISBN 9788245026566. 600 p. Full text in Research Archive
Dovland, Olav Kristian & Pettersen, Petter (2019). Reelle tall i arbeid. Fagbokforlaget. ISBN 9788245032062. 308 p. Full text in Research Archive
Dovland, Olav Kristian Gunnarson & Pettersen, Petter (2015). Matematikk for økonomistudenter, 2. utgave. Fagbokforlaget. ISBN 9788245018028. 574 p. Full text in Research Archive
Nygaard, Olav Kristian & Pettersen, Petter (2014). Matematikk for økonomistudenter. Fagbokforlaget. ISBN 9788245016802. 528 p. Full text in Research Archive
Hundeland, Per Sigurd; Nygaard, Olav Kristian; Nygaard, Olav Kristian & Pettersen, Petter (2001). Matematikk for økonomi og samfunnsfag - aktuelle eksamensoppgaver med løsninger. Cappelen Damm Høyskoleforlaget. ISBN 9788276343458. 195 p. Full text in Research Archive
Nygaard, Olav; Nygaard, Olav & Pettersen, Petter (2000). Fatte matte : for deg som vil tette huller i elementære matematikkunnskaper. Cappelen Damm Høyskoleforlaget. ISBN 9788276343151. 174 p. Full text in Research Archive
Nygaard, Olav; Nygaard, Olav; Hundeland, Per Sigurd & Pettersen, Petter (1999). AHA Matematikk og matematikkdidaktikk. Cappelen Damm Høyskoleforlaget. ISBN 9788276342635. 719 p. Full text in Research Archive Show summary
Boka er skreddersydd for det obligatoriske tivekttallskurset i matematikk i norsk lærerutdanning. Den dekker alle grunnskolens matematikkemner og inneholder didaktiske refleksjoner omkring disse. The book is intended for a half-year compulsory course in didactics of mathematics and mathematics in Norwegian teacher's training. All basic subjects relevant for public school is covered together with didactical reflections on the subjects.
Nygaard, Olav; Nygaard, Olav; Pettersen, Petter & Hundeland, Per Sigurd (1999). AHA Matematikk og Matematikkdidaktikk Fasit til 2. utgave. Cappelen Damm Høyskoleforlaget. ISBN 9788276342659. 72 p. Full text in Research Archive
Nygaard, Olav; Nygaard, Olav; Hundeland, Per Sigurd & Pettersen, Petter (1998). AHA Matematikk og matematikkdidaktikk. Cappelen Damm Høyskoleforlaget. ISBN 9788276341430. 714 p. Full text in Research Archive Show summary
Boka er skreddersydd for det obligatoriske tivektallskurset i matemat ikk i norsk lærerutdanning. Den dekker alle grunnskolens matematikkem ner og inneholder didaktiske refleksjoner omkring disse. The book is intended for a half-year compulsory course in didactics o f mathematics and mathematics in Norwegian teacher's training. All ba sic subje relevant for public school is covered together with didacti cal reflections on the subjects.

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Dovland, Olav Kristian Gunnarson (2022). Convexity and big slices. Full text in Research Archive Show summary
We give an overview of recent result concerning how strong convexity properties can co-exist with various diameter two properties.
Nygaard, Olav Kristian (2016). Vegusdal kyrkje 150 år i 2017. Årsskrift - Birkenes historielag. ISSN 0800-3033. p. 55–56. Full text in Research Archive
Nygaard, Olav Kristian & Vellene, Jens (2016). Ord frå Vegusdalsdialekten, del 4. Årsskrift - Birkenes historielag. ISSN 0800-3033. p. 103–104. Full text in Research Archive
Abrahamsen, Trond Arnold; Langemets, Johann; Lima, Vegard & Nygaard, Olav Kristian (2015). Correction to the paper On thickness and thinness in Banach spaces, Houston J. Math., 41 (2015), no. 1, 97-111. Houston Journal of Mathematics. ISSN 0362-1588. 41(4), p. 1359–1360. Full text in Research Archive
Nygaard, Olav Kristian & Vellene, Jens (2014). Ord frå Vegusdalsdialekten, del 2. Årsskrift - Birkenes historielag. ISSN 0800-3033. 33, p. 49–52. Full text in Research Archive
Nygaard, Olav Kristian (2014). On a problem of M. Valdivia. Full text in Research Archive
Nygaard, Olav Kristian (2014). Ueber Whitney's Dichtheitsindex. Full text in Research Archive
Nygaard, Olav Kristian (2013). The symmetric strong diameter 2 property II. Full text in Research Archive
Nygaard, Olav Kristian & Vellene, Jens (2013). Ord frå Vegusdalsdialekten. Årsskrift - Birkenes historielag. ISSN 0800-3033. 32, p. 30–35. Full text in Research Archive
Nygaard, Olav Kristian (2013). Diameter 2 Eigenschaften in Banach Raeume. Full text in Research Archive
Nygaard, Olav Kristian (2013). Heim til Vegusdal. Årsskrift - Birkenes historielag. ISSN 0800-3033. 32, p. 10–11. Full text in Research Archive
Nygaard, Olav Kristian (2013). The symmetric strong diameter 2 property I. Full text in Research Archive
Nygaard, Olav Kristian (2012). Diameter 2 properties in Banach spaces. Full text in Research Archive
Nygaard, Olav Kristian (2012). Ei lita gåte frå Mykland - med svar frå Vegusdal og Herefoss. Årsskrift - Birkenes historielag. ISSN 0800-3033. 31, p. 74–76. Full text in Research Archive
Nygaard, Olav Kristian (2012). Diameter 2 properties in Banach spaces: Overview and some problems. Full text in Research Archive
Nygaard, Olav (2011). How does the unit ball in a Banach space look? Full text in Research Archive
Nygaard, Olav Kristian (2011). Den vonde dansen. Årsskrift - Birkenes historielag. ISSN 0800-3033. 30, p. 19–22. Full text in Research Archive
Nygaard, Olav Kristian (2008). Geometry in the unit ball of the Hardy space H^1. Full text in Research Archive Show summary
We describe the extremal structure of the unit ball of H^1 due to Rudin and de Leeuw. On our way we focus on the celebrated factorization theorem of Arne Beurling.
Nygaard, Olav Kristian (2005). Fatte Matte, både som barn og voksen. Full text in Research Archive Show summary
Om misforståelser i matematisk tenking. Tanker om en type pedagogikk som kan rette på dette.
Nygaard, Olav Kristian (2004). Sequential properties of the weak topology in a Banach space. Full text in Research Archive Show summary
We will prove the Eberlein-Smulian theorem. Along with this we will speak about weak convergence of bounded sequences. Finally we will introduce the concept of "(I)-generating set", "Rainwater set" and "James boundary" and tell some story about these kind of sets, in particular we indicate a proof of James' characterization of reflexive spaces for weakly compactly generated spaces.
Nygaard, Olav Kristian (2004). Some open problems concerning massiveness. Full text in Research Archive
Nygaard, Olav Kristian (2003). On weak integrability. Full text in Research Archive
Nygaard, Olav (2000). Slices in the unit ball of a uniform algebra. Full text in Research Archive Show summary
We show that if the unit ball of a uniform algebra is divided into two parts by a hyperplane such that each part contains more than one point, than both parts will necessarily have diameter 2.
Martiny, Andre; Abrahamsen, Trond Arnold; Lima, Vegard & Dovland, Olav Kristian (2021). The big slice phenomenon in Banach spaces. Universitetet i Agder. ISSN 9788284270418. Full text in Research Archive
Nygaard, Olav Kristian (2017). Vegusdal kyrkje på Engesland 150 år. Vegusdal sokneråd. Full text in Research Archive
Nygaard, Olav Kristian (2007). Begreper i analyse. Universitetet i Agder. Full text in Research Archive Show summary
Heftet danner pensum i kurset Begreper i analyse ved Universitetet i Agder
Storesletten, Leiv & Nygaard, Olav Kristian (2005). Matematisk Modellering. Andre utgåve. Universitetet i Agder. Full text in Research Archive
Storesletten, Leiv & Nygaard, Olav Kristian (2004). Matematisk Modellbygging. Universitetet i Agder. Full text in Research Archive
Nygaard, Olav Kristian (2001). Approximation, Boundedness, Surjectivity. Full text in Research Archive

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Published Apr. 16, 2024 11:00 AM