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Currently displaying 1 – 2 of 2

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On the scooping property of measures by means of disjoint balls

Elena Riss — 1996

Acta Universitatis Carolinae. Mathematica et Physica

On $r$ -reflexive Banach spaces

Iryna Banakh; Taras O. Banakh; Elena Riss — 2009

Commentationes Mathematicae Universitatis Carolinae

A Banach space $X$ is called if for any cover $𝒰$ of $X$ by weakly open sets there is a finite subfamily $𝒱 \subset 𝒰$ covering some ball of radius 1 centered at a point $x$ with $∥ x ∥ \leq r$ . We prove that an infinite-dimensional separable Banach space $X$ is $\infty$ -reflexive ( $r$ -reflexive for some $r \in ℕ$ ) 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 $r \in ℕ$ . We do not know if each $\infty$ -reflexive...

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