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FUNCTIONS ATTAINING THE SUPREMUM AND ISOMORPHIC PROPERTIES OF A BANACH SPACE
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 Title & Authors
FUNCTIONS ATTAINING THE SUPREMUM AND ISOMORPHIC PROPERTIES OF A BANACH SPACE
D. Acosta, Maria ; Becerra Guerrero, Julio ; Ruiz Galan, Manuel;
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 Abstract
We prove that a Banach space that is convex-transitive and such that for some element u in the unit sphere, and for every subspace Μ containing u, it happens that the subset of norm attaining functionals on Μ is second Baire category in is, in fact, almost-transitive and superreflexive. We also obtain a characterization of finite-dimensional spaces in terms of functions that attain their supremum: a Banach space is finite-dimensional if, for every equivalent norm, every rank-one operator attains its numerical radius. Finally, we describe the subset of norm attaining functionals on a space isomorphic to , where the norm is the restriction of a Luxembourg norm on . In fact, the subset of norm attaining functionals for this norm coincides with the subset of norm attaining functionals for the usual norm.m.
 Keywords
reflexive Banach spaces;norm attaining functionals;convex-transitive Banach spaces;almost-transitive Banach spaces;numerical radius attaining operators;Luxembourg norm;smooth norm;
 Language
English
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