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Zbl 0814.46043
Chu, Cho-Ho
The weak Banach-Saks property in $C\sp*$-algebras. (English)
[J] J. Funct. Anal. 121, No.1, 1-14 (1994). ISSN 0022-1236

It is shown that a $C\sp*$-algebra ${\bold A}$ has the weak Banach-Saks property if and only if it is type I and the $k$th-derivative of its spectrum $\widehat{{\bold A}}$ is empty for some $k$. This is equivalent to the existence of a finite chain $J\sb 1\subset J\sb 2\subset\cdots\subset J\sb n\subset {\bold A}$ of closed ideals such that $J\sb 1, J\sb 2/J\sb 1,\dots, {\bold A}/J\sb n$ are all dual $C\sp*$- algebras.

MSC 2000:: *46L05 General theory of C*-algebras
46B22 Spaces with Radon-Nikodym property

Keywords: $C\sp*$-algebra; Banach-Saks property; closed ideals; dual $C\sp*$- algebras

Cited in: Zbl 1206.46009

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