Topological centers of certain dual algebras

Lau, Anthony; Ülger, Ali

doi:10.1090/S0002-9947-96-01499-7

Topological centers of certain dual algebras
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by Anthony To-Ming Lau and Ali Ülger PDF

Trans. Amer. Math. Soc. 348 (1996), 1191-1212 Request permission

Abstract:

Let $A$ be a Banach algebra with a bounded approximate identity. Let $Z_1$ and $\widetilde Z_2$ be, respectively, the topological centers of the algebras $A^{**}$ and $(A^*A)^*$. In this paper, for weakly sequentially complete Banach algebras, in particular for the group and Fourier algebras $L^1(G)$ and $A(G)$, we study the sets $Z_1$, $\widetilde Z_2$, the relations between them and with several other subspaces of $A^{**}$ or $A^*$.

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