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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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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Additional Information

Anthony To-Ming Lau
Affiliation: Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
Email: tlau@vega.math.ualberta.ca

Ali Ülger
Affiliation: Department of Mathematics, Boḡazici University, 80815 Bebek-Istanbul, Turkey
Email: ulger@boun.edu.tr

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01499-7
PII: S 0002-9947(96)01499-7
Keywords: Topological center, multiplier algebra, group algebra and Fourier algebra
Received by editor(s): September 4, 1994
Received by editor(s) in revised form: March 27, 1995
Additional Notes: The research of the first author is supported by an NSERC grant.
The research of the second author is supported by TUBA
Article copyright: © Copyright 1996 American Mathematical Society