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hilbert $c^*$-module

Proceedings of the Edinburgh Mathematical Society (1)

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MORITA EQUIVALENCE FOR C*-ALGEBRAS WITH THE WEAK BANACH–SAKS PROPERTY. II
Masaharu Kusuda
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 50 / Issue 1 / February 2007

Published online by Cambridge University Press:

09 February 2007, pp. 185-195
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Let $C^*$-algebras $A$ and $B$ be Morita equivalent and let $X$ be an $A$–$B$-imprimitivity bimodule. Suppose that $A$ or $B$ is unital. It is shown that $X$ has the weak Banach–Saks property if and only if it has the uniform weak Banach–Saks property. Thus, we conclude that $A$ or $B$ has the weak Banach–Saks property if and only if $X$ does so. Furthermore, when $C^*$-algebras $A$ and $B$ are unital, it is shown that $X$ has the Banach–Saks property if and only if it is finite dimensional.