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arXiv · 2006.03823

Characterization of Symmetric Amenability of Unital Banach Algebras

Ali Jabbari·Ali Ebadian
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Abstract

In this paper, we introduce $p$-amenability, bounded $s$-symmetric approximate and $s$-symmetric virtual diagonals for a Banach algebra $\mathfrak{A}$ where $s$ is a non-zero element of algebraic center of $\mathfrak{A}$ that is denoted by $Z(\mathfrak{A})$. We show that if a Banach algebra $\mathfrak{A}$ is $p$-amenable then it has bounded $s$-symmetric approximate and $s$-symmetric virtual diagonals and by this fact we prove that if the Banach algebra $\mathfrak{A}$ is unital then $p$-amenability and symmetric amenability are equivalent.

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BibTeXRIS

Ali Jabbari, Ali Ebadian. 2020-06-06. Characterization of Symmetric Amenability of Unital Banach Algebras. https://arxiv.org/abs/2006.03823

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