39 citations · 49 across the 12 of their papers we have counts for
19 papers
Duality of Lipschitz-free spaces over ultrametric spaces
Trond A. Abrahamsen, Vegard Lima, Andre Ostrak
We give a metric characterisation of when the Lipschitz-free space over a separable ultrametric space is a dual Banach space. In the case where the Lipschitz-free space has a predu…
Strictly convex norms and the local diameter two property
Trond A. Abrahamsen, Petr Hájek, Vegard Lima +1
We introduce and study a strict monotonicity property of the norm in solid Banach lattices of real functions that prevents such spaces from having the local diameter two property.…
A relative version of Daugavet-points and the Daugavet property
Trond A. Abrahamsen, Ramón J. Aliaga, Vegard Lima +4
We introduce relative versions of Daugavet-points and the Daugavet property, where the Daugavet-behavior is localized inside of some supporting slice. These points present striking…
Delta-points and their implications for the geometry of Banach spaces
Trond A. Abrahamsen, Ramón J. Aliaga, Vegard Lima +4
We show that the Lipschitz-free space with the Radon--Nikodým property and a Daugavet point recently constructed by Veeorg is in fact a dual space isomorphic to . Furthermo…
Asymptotic geometry and delta-points
Trond A. Abrahamsen, Vegard Lima, André Martiny +1
We study Daugavet- and -points in Banach spaces. A norm one element is a Daugavet-point (respectively a -point) if in every slice of the unit ball (respectively in every…
Delta-points in Banach spaces generated by adequate families
Trond A. Abrahamsen, Vegard Lima, André Martiny
We study delta-points in Banach spaces generated by adequate families where . In the case the familiy is regular and…
Daugavet- and delta-points in Banach spaces with unconditional bases
Trond A. Abrahamsen, Vegard Lima, André Martiny +1
We study the existence of Daugavet- and delta-points in the unit sphere of Banach spaces with a -unconditional basis. A norm one element in a Banach space is a Daugavet-poin…
On Daugavet indices of thickness
Rainis Haller, Johann Langemets, Vegard Lima +2
Inspired by R. Whitley's thickness index the last named author recently introduced the Daugavet index of thickness of Banach spaces. We continue the investigation of the behavior o…
Delta- and Daugavet-points in Banach spaces
Trond Arnold Abrahamsen, Rainis Haller, Vegard Lima +1
A -point of a Banach space is a norm one element that is arbitrarily close to convex combinations of elements in the unit ball that are almost at distance from . If,…
Banach spaces where convex combinations of relatively weakly open subsets of the unit ball are relatively weakly open
Trond Arnold Abrahamsen, Julio Becerra Guerrero, Rainis Haller +2
We introduce and study Banach spaces which have property CWO, i.e., every finite convex combination of relatively weakly open subsets of their unit ball is open in the relative wea…
Symmetric strong diameter two property
Rainis Haller, Johann Langemets, Vegard Lima +1
We study Banach spaces with the property that, given a finite number of slices of the unit ball, there exists a direction such that all these slices contain a line segment of lengt…
Relatively weakly open convex combinations of slices
Trond A. Abrahamsen, Vegard Lima
We show that , and in fact for any scattered compact Hausdorff space , have the property that finite convex combinations of slices of the unit ball are relatively we…
Diameter two properties, convexity and smoothness
Trond A. Abrahamsen, Vegard Lima, Olav Nygaard +1
We study smoothness and strict convexity of (the bidual) of Banach spaces in the presence of diameter 2 properties. We prove that the strong diameter 2 property prevents the bidual…
Almost square and octahedral norms in tensor products of Banach spaces
Johann Langemets, Vegard Lima, Abraham Rueda Zoca
The aim of this note is to study some geometrical properties like diameter two properties, octahedrality and almost squareness in the setting of (symmetric) tensor product spaces.…
On thickness and thinness of Banach spaces
Trond A. Abrahamsen, Johann Langemets, Vegard Lima +1
The aim of this note is to complement and extend some recent results on Whitley's indices of thinness and thickness in three main directions. Firstly, we investigate both the indic…
Almost square Banach spaces
Trond A. Abrahamsen, Johann Langemets, Vegard Lima
We single out and study a natural class of Banach spaces -- almost square Banach spaces. In an almost square space we can find, given a finite set in the unit…
Remarks on diameter 2 properties
Trond Abrahamsen, Vegard Lima, Olav Nygaard
If is an infinite-dimensional uniform algebra, if has the Daugavet property or if is a proper -embedded space, every relatively weakly open subset of the unit ball o…
Almost isometric ideals in Banach spaces
Trond A. Abrahamsen, Vegard Lima, Olav Nygaard
A natural class of ideals, almost isometric ideals, of Banach spaces is defined and studied. The motivation for working with this class of subspaces is our observation that they in…
Property and uniform quotient maps
Vegard Lima, N. Lovasoa Randrianarivony
In 1999, Bates, Johnson, Lindenstrauss, Preiss and Schechtman asked whether a Banach space that is a uniform quotient of , , must be isomorphic to a…