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arXiv · 2104.01559

Center of Banach algebra valued Beurling algebras

Bharat Talwar·Ranjana Jain
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Abstract

We prove that for a Banach algebra $A$ having a bounded $\mathcal{Z}(A)$-approximate identity and for every $\bf[IN]$ group $G$ with weight $w$ which is either constant on conjugacy classes or $w \geq 1$, $\mathcal{Z}\big(L^1_w(G) \otimes^\gamma A\big) \cong \mathcal{Z}(L^1_w(G)) \otimes^\gamma \mathcal{Z}(A)$. As an application, we discuss the conditions under which $\mathcal{Z}\big(L^1_w(G,A)\big)$ enjoys certain Banach algebraic properties, for example, weak amenability, semisimplicity etc.

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Bharat Talwar, Ranjana Jain. 2021-04-04. Center of Banach algebra valued Beurling algebras. https://doi.org/10.1017/s0004972721000691

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