On duality of diameter 2 properties

R Haller, J Langemets, M Põldvere - arXiv preprint arXiv:1311.2177, 2013 - arxiv.org
It is known that a Banach space has the strong diameter 2 property (ie every convex
combination of slices of the unit ball has diameter 2) if and only if the norm on its dual space …

[HTML][HTML] Almost square Banach spaces

TA Abrahamsen, J Langemets, V Lima - Journal of Mathematical Analysis …, 2016 - Elsevier
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 x 1, x 2,…, x N in the unit sphere, a …

Symmetric strong diameter two property

R Haller, J Langemets, V Lima, R Nadel - Mediterranean Journal of …, 2019 - Springer
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 length almost …

Diameter 2 properties and convexity

TA Abrahamsen, P Hájek, O Nygaard… - arXiv preprint arXiv …, 2015 - arxiv.org
We present an equivalent midpoint locally uniformly rotund (MLUR) renorming $ X $ of $ C
[0, 1] $ on which every weakly compact projection $ P $ satisfies the equation $\| IP\|= 1+\| P …

New applications of extremely regular function spaces

T Abrahamsen, O Nygaard, M Põldvere - Pacific Journal of Mathematics, 2019 - msp.org
Let L be an infinite locally compact Hausdorff topological space. We show that extremely
regular subspaces of C 0 (L) have very strong diameter 2 properties and, for every real …

Linear extensions, almost isometries, and diameter two

TA Abrahamsen - extracta mathematicae, 2015 - revista-em.unex.es
Heinrich, Mankiewicz, Sims, and Yost proved that every separable subspace of a Banach
space Y is contained in a separable ideal in Y. We improve this result by replacing the term …

Stability of diametral diameter two properties

J Langemets, K Pirk - Revista de la Real Academia de Ciencias Exactas …, 2021 - Springer
We prove that the diametral diameter two properties are inherited by F-ideals (eg, M-ideals).
On the other hand, these properties are lifted from an M-ideal to the superspace under …

[PDF][PDF] Diametral diameter two properties, Daugavet-, and Δ-points in Banach spaces

K Pirk - Dissertationes Mathematicae Universitatis Tartuensis, 2020 - core.ac.uk
KATRIIN PIRK Diametral diameter two properties, Daugavet-, and Δ-points in Banach
spaces Page 1 I DISSERTATIONES MATHEMATICAE UNIVERSITATIS TARTUENSIS 133 …

Summands in locally almost square and locally octahedral spaces

JD Hardtke - arXiv preprint arXiv:1705.06610, 2017 - arxiv.org
arXiv:1705.06610v2 [math.FA] 24 Nov 2017 Page 1 arXiv:1705.06610v2 [math.FA] 24 Nov
2017 November 1, 2021 Summands in locally almost square and locally octahedral spaces …

Relatively weakly open convex combinations of slices

T Abrahamsen, V Lima - Proceedings of the American Mathematical …, 2018 - ams.org
Relatively weakly open convex combinations of slices Page 1 PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 146, Number 10, October 2018, Pages …