Unrestricted products of contractions in Banach spaces

Details Unrestricted products of contractions in Banach spaces Unrestricted products of contractions in Banach spaces

1992-10-30

arxiv.org/abs/math/9210211v1

Mathematics

Functional Analysis

Scientific paper

Let $X$ be a reflexive Banach space such that for any $x \ne 0$ the set $$
\{x^* \in X^*: \text {$\|x^*\|=1$ and $x^*(x)=\|x\|$}\} $$ is compact. We
prove that any unrestricted product of of a finite number of $(W)$
contractions on $X$ converges weakly.

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