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On r -reflexive Banach spaces

Iryna Banakh, Taras O. Banakh, Elena Riss (2009)

Commentationes Mathematicae Universitatis Carolinae

A Banach space X is called r -reflexive if for any cover 𝒰 of X by weakly open sets there is a finite subfamily 𝒱 𝒰 covering some ball of radius 1 centered at a point x with x r . We prove that an infinite-dimensional separable Banach space X is -reflexive ( r -reflexive for some r ) if and only if each ε -net for X has an accumulation point (resp., contains a non-trivial convergent sequence) in the weak topology of X . We show that the quasireflexive James space J is r -reflexive for no r . We do not know...

On rank one elements

Robin Harte (1995)

Studia Mathematica

Without the "scarcity lemma", two kinds of "rank one elements" are identified in semisimple Banach algebras.

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