Amenability properties of Banach algebra valued continuous functions
type: Item
instance of: scholarly article
title: Amenability properties of Banach algebra valued continuous functions
zbMATH Open document ID: 1310.46042
author: Reza Ghamarshoushtari
author: Yong Zhang
published in: Journal of Mathematical Analysis and Applications
publication date: 2014-10-31T00:00:00Z
full work available at URL: https://arxiv.org/abs/2001.08148
review text: Let \(X\) be a compact Hausdorff space and \(A\) a Banach algebra. It is well known that \(C(X)=C(X, \mathbb{C}) \) is amenable for any compact Hausdorff space \(X\). The authors investigate amenability properties of the Banach algebra \(C(X,A)\) of all \(A\)-valued continuous functions on \(X\) endowed with the uniform norm \(\|f\|_{\infty} = \sup \left\{ \|f(x) \|_A : x \in X \right\},\) \(f \in C(X,A)\). As results, they prove that \(C(X,A)\) is amenable if and only if \(A\) is amenable; \(C(X,A)\) has a compactly approximate diagonal if \(A\) has a central compactly approximate diagonal; and \(C(X,A)\) is weakly amenable if \(A\) is a commutative weakly amenable Banach algebra with a bounded approximate identity.
reviewed by: Hark-Mahn Kim
Mathematics Subject Classification ID: 46H20
Mathematics Subject Classification ID: 46H25
zbMATH DE Number: 6362878
zbMATH Keywords: abstract continuous functions
zbMATH Keywords: amenability
zbMATH Keywords: approximate diagonal
zbMATH Keywords: weak amenability
zbMATH Keywords: Banach algebra
MaRDI profile type: Publication
OpenAlex ID: W3001830806
arXiv ID: 2001.08148
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DOI: 10.1016/J.JMAA.2014.09.042
description: scientific article; zbMATH DE number 6362878