Topological centers of certain dual algebras

Lau, Anthony; Ülger, Ali

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

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Topological centers of certain dual algebras

Authors: Anthony To-Ming Lau and Ali Ülger
Journal: Trans. Amer. Math. Soc. 348 (1996), 1191-1212
MSC (1991): Primary 43A20; Secondary 46H05
MathSciNet review: 1322952
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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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