Vegard Lima

• Abrahamsen, Trond Arnold; Lima, Vegard & Martiny, Andre (2022). Delta-points in Banach spaces generated by adequate families. Illinois Journal of Mathematics. ISSN 0019-2082. 66(3), p. 421–434. doi: 10.1215/00192082-10123638.
• Abrahamsen, Trond Arnold; Lima, Vegard; Martiny, Andre & Perreau, Yoël (2022). Asymptotic geometry and Delta-points. Banach Journal of Mathematical Analysis. ISSN 2662-2033. 16. doi: 10.1007/s43037-022-00210-9. Full text in Research Archive Show summary

  We study Daugavet- and Δ-points in Banach spaces. A norm one element x is a Daugavet-point (respectively, a Δ-point) if in every slice of the unit ball (respectively, in every slice of the unit ball containing x) you can find another element of distance as close to 2 from x as desired. In this paper, we look for criteria and properties ensuring that a norm one element is not a Daugavet- or Δ-point. We show that asymptotically uniformly smooth spaces and reflexive asymptotically uniformly convex spaces do not contain Δ-points. We also show that the same conclusion holds true for the James tree space as well as for its predual. Finally, we prove that there exists a superreflexive Banach space with a Daugavet- or Δ-point provided there exists such a space satisfying a weaker condition.

• Haller, Rainis; Langemets, Johann; Lima, Vegard; Nadel, Rihhard & Rueda Zoca, Abraham (2021). On Daugavet indices of thickness. Journal of Functional Analysis. ISSN 0022-1236. 280(7), p. 1–21. doi: 10.1016/j.jfa.2020.108846. Full text in Research Archive
• Abrahamsen, Trond Arnold; Lima, Vegard; Martiny, Andre & Troyanski, Stanimir (2021). Daugavet- and delta-points in Banach spaces with unconditional bases. Transactions of the American Mathematical Society - Series B. ISSN 2330-0000. 8(13), p. 379–398. doi: 10.1090/btran/68. Full text in Research Archive
• Abrahamsen, Trond Arnold; Haller, Rainis; Lima, Vegard & Pirk, Katriin (2020). Delta- and Daugavet points in Banach spaces. Proceedings of the Edinburgh Mathematical Society. ISSN 0013-0915. 63(2), p. 475–496. doi: 10.1017/S0013091519000567. Full text in Research Archive
• Abrahamsen, Trond Arnold; Becerra Guerrero, Julio; Haller, Rainis; Lima, Vegard & Poldvere, Mert (2020). Banach spaces where convex combinations of relatively weakly open subsets of the unit ball are relatively weakly open. Studia Mathematica. ISSN 0039-3223. 250(3), p. 297–320. doi: 10.4064/sm181016-10-1. Full text in Research Archive
• Haller, Rainis; Langemets, Johann; Lima, Vegard & Nadel, Rihhard (2019). Symmetric strong diameter two property. Mediterranean Journal of Mathematics. ISSN 1660-5446. 16:35(2), p. 1–17. doi: 10.1007/s00009-019-1306-1. Full text in Research Archive
• Abrahamsen, Trond Arnold & Lima, Vegard (2018). Relatively weakly open convex combinations of slices. Proceedings of the American Mathematical Society. ISSN 0002-9939. 146(10), p. 4421–4427. doi: 10.1090/proc/14120. Full text in Research Archive
• Langemets, Johann; Lima, Vegard & Zoca, Abraham Rueda (2017). Octahedral norms in tensor products of Banach spaces. Quarterly Journal of Mathematics. ISSN 0033-5606. 68(4), p. 1247–1260. doi: 10.1093/qmath/hax020.
• Langemets, Johann; Lima, Vegard & Rueda Zoca, Abraham (2017). Almost square and octahedral norms in tensor products of Banach spaces . Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. ISSN 1578-7303. 111(3), p. 841–853. doi: 10.1007/s13398-016-0324-0. Full text in Research Archive
• 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.
• Abrahamsen, Trond Arnold; Langemets, Johann & Lima, Vegard (2016). Almost square Banach spaces. Journal of Mathematical Analysis and Applications. ISSN 0022-247X. 434(2), p. 1549–1565. doi: 10.1016/j.jmaa.2015.09.060.
• 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.
• 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.
• Lima, Åsvald; Lima, Vegard & Oja, Eve (2014). Absolutely summing operators on separable lindenstrauss spaces as tree spaces and the bounded approximation property. Banach Journal of Mathematical Analysis. ISSN 2662-2033. 8(1), p. 190–210.
• Abrahamsen, Trond Arnold; Lima, Vegard & Dovland, Olav (2013). Remarks on diameter 2 properties. Journal of Convex Analysis. ISSN 0944-6532.
• 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.
• Lima, Åsvald; Lima, Vegard & Oja, Eve (2012). BOUNDED APPROXIMATION PROPERTIES IN TERMS OF C[0,1]. Mathematica Scandinavica. ISSN 0025-5521. 110(1), p. 45–58. doi: 10.7146/math.scand.a-15195. Show summary

• Lima, Vegard & Randrianarivony, N. Lovasoa (2012). Property (beta) and uniform quotient maps. Israel Journal of Mathematics. ISSN 0021-2172. 192(1), p. 311–323. doi: 10.1007/s11856-012-0025-0.
• Lima, Åsvald; Lima, Vegard & Oja, Eve (2010). Absolutely summing operators on C[0,1] as a tree space and the bounded approximation property. Journal of Functional Analysis. ISSN 0022-1236. 259(11), p. 2886–2901. Show summary

  Let X be a Banach space. For describing the space of absolutely summing operators from C[0,1] to X in terms of the space X itself, we construct a tree space on X. It consists of special trees in X which we call two-trunk trees. We prove that is isometrically isomorphic to . As an application, we characterize the bounded approximation property (BAP) and the weak BAP in terms of X*-valued sequence spaces.

• Lima, Åsvald; Lima, Vegard & Oja, Eve (2010). Bounded approximation properties via integral and nuclear operators. Proceedings of the American Mathematical Society. ISSN 0002-9939. 138(1), p. 287–297. Show summary

  Let $X$ be a Banach space and let $mathcal A$ be a Banach operator ideal. We say that $X$ has the $lambda $-bounded approximation property for $mathcal A$ ($lambda $-BAP for $mathcal A$) if for every Banach space $Y$ and every operator $Tin mathcal A(X,Y)$, there exists a net $(S_alpha )$ of finite rank operators on $X$ such that $S_alpha to I_X$ uniformly on compact subsets of $X$ and $$limsup _alpha |TS_alpha |_{mathcal A}leq lambda |T|_{mathcal A}.$$ We prove that the (classical) $lambda $-BAP is precisely the $lambda $-BAP for the ideal

• Abrahamsen, Trond Arnold; Lima, Vegard & Lima, Åsvald (2009). UNCONDITIONAL IDEALS OF FINITE RANK OPERATORS II. Houston Journal of Mathematics. ISSN 0362-1588. 35(2), p. 627–646. Show summary

  Let E be a subspace of a normed space F. It is known that E is an ideal (resp. a u-ideal) in F if and only if E is an ideal (resp. a u-ideal) in G for every subspace E subset of G subset of F in which E has finite codimension (resp. codimension <= 2). We show that in many cases a space of finite rank operators is an ideal (resp. a u-ideal) in a larger space if and only if it is an ideal (resp. a u-ideal) in a space in which it has codimension 1. In particular, we show that F(Y, X) is an ideal (resp. a u-ideal) in W (Y, X **) for all Banach spaces Y if and only if for every reflexive Banach space Y and T is an element of W (Y, X **), F(Y, X) is an ideal (resp. a u-ideal) in span (F(Y, X), {T}).

• Lima, Vegard & Lima, Åsvald (2009). Strict u-ideals in Banach spaces. Studia Mathematica. ISSN 0039-3223. 195(3), p. 275–285. doi: 10.4064/sm195-3-6. Show summary

  We study strict u-ideals in Banach spaces. A Banach space X is a strict u-ideal in its bidual when the canonical decomposition X = X X? is unconditional.We characterize Banach spaces which are strict u-ideals in their bidual and show that if X is a strict u-ideal in a Banach space Y then X contains c0. We also show that `1 is not a u-ideal. Vi karakteriserer Banachrom som er strikte u-idealer i sitt biduale.

• Lima, Åsvald; Abrahamsen, Trond Arnold & Lima, Vegard (2008). Unconditional ideals of finite rank operators. Czechoslovak Mathematical Journal. ISSN 0011-4642. 58(4), p. 1257–1278.
• Lima, Åsvald & Lima, Vegard (2008). Geometry of spaces of compact operators. Arkiv för matematik. ISSN 0004-2080. 46(1), p. 113–142. doi: 10.1007/s11512-007-0060-y. Show summary

  We introduce the notion of compactly locally reflexive Banach spaces and show that a Banach space X is compactly locally reflexive if and only if K(Y, X**) subset of K(Y, X)** for all reflexive Banach spaces Y. We show that X* has the approximation property if and only if X has the approximation property and is compactly locally reflexive. The weak metric approximation property was recently introduced by Lima and Oja. We study two natural weak compact versions of this property. If X is compactly locally reflexive then these two properties coincide. We also show how these properties are related to the compact approximation property and the compact approximation property with conjugate operators for dual spaces.

• Lima, Åsvald & Lima, Vegard (2007). A three-ball intersection property for u-ideals. Journal of Functional Analysis. ISSN 0022-1236. 252(1), p. 220–232. Show summary

  First introduced by Casazza and Kalton, u-ideals are generalizations of M-ideals. We characterize u-ideals of Banach spaces using intersection properties of balls. We also give axamples showing that our results are best possible.

• Lima, Vegard & Lima, Åsvald (2004). Ideals of operators and the metric approximation property. Journal of Functional Analysis. ISSN 0022-1236. 210(1), p. 148–170.
• Lima, Åsvald; Lima, Vegard & Nygaard, Olav Kristian (2004). On the compact approximation property. Studia Mathematica. ISSN 0039-3223. 160(2), p. 185–200.
• Lima, Vegard (2003). Approximation properties for dual spaces. Mathematica Scandinavica. ISSN 0025-5521. 93(2), p. 297–319.

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• Gjesteland, Thomas; Lima, Vegard; Lunøe-Nielsen, Sverre A; Radmehr, Farzad & Goodchild, Simon (2021). Gruppebasert prosjektoppgave i matematikk: Veiledernes erfaringer.
• Lima, Vegard (2019). Banach spaces where convex combinations of slices are relatively weakly open.
• 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.
• Lima, Vegard (2014). Banach spaces -- through thick and thin.
• 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
• Lima, Vegard (2004). Ideals of operators and the approximation property. ISSN 8292160299.

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