Back to Search Start Over

Almost square Banach spaces.

Authors :
Abrahamsen, Trond A.
Langemets, Johann
Lima, Vegard
Source :
Journal of Mathematical Analysis & Applications. Feb2016, Vol. 434 Issue 2, p1549-1565. 17p.
Publication Year :
2016

Abstract

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 unit vector y such that ‖ x i − y ‖ is almost one. These spaces have duals that are octahedral and finite convex combinations of slices of the unit ball of an almost square space have diameter 2. We provide several examples and characterizations of almost square spaces. We prove that non-reflexive spaces which are M -ideals in their biduals are almost square. We show that every separable space containing a copy of c 0 can be renormed to be almost square. A local and a weak version of almost square spaces are also studied. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
0022247X
Volume :
434
Issue :
2
Database :
Academic Search Index
Journal :
Journal of Mathematical Analysis & Applications
Publication Type :
Academic Journal
Accession number :
110559239
Full Text :
https://doi.org/10.1016/j.jmaa.2015.09.060