Center of Banach algebra valued Beurling algebras

Abstract

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

10 pages

References in corpus (2)

• On closed Lie ideals and center of generalized group algebras
• Lattice of intermediate subalgebras