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arXiv · 2001.08148

Amenability properties of Banach algebra valued continuous functions

Reza Ghamarshoushtari·Yong Zhang
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Abstract

Let $X$ be a compact Hausdorff space and $A$ a Banach algebra. We investigate amenability properties of the algebra $C(X,A)$ of all $A$-valued continuous functions. We show that $C(X,A)$ has a bounded approximate diagonal if and only if $A$ has a bounded approximate diagonal; if $A$ has a compactly central approximate diagonal (unbounded) then $C(X,A)$ has a compactly approximate diagonal. Weak amenability of $C(X,A)$ for commutative $A$ is also considered.

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BibTeXRIS

Reza Ghamarshoushtari, Yong Zhang. 2020-01-22. Amenability properties of Banach algebra valued continuous functions. https://arxiv.org/abs/2001.08148

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