Arens regularity of ideals in $A(G)$, $A_{cb}(G)$ and $A_M(G)$.

Document Type : Dedicated to Prof. A. T.-M. Lau

Authors

Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1.

Abstract

In this paper, we look at the question of when various ideals in the Fourier algebra $A(G)$ or its closures $A_M(G)$ and $A_{cb}(G)$ in, respectively, its multiplier and $cb$-multiplier algebra are Arens regular. We show that in each case, if a non-zero ideal is Arens regular, then the underlying group $G$ must be discrete. In addition, we show that if an ideal $I$ in $A(G)$ has a bounded approximate identity, then it is Arens regular if and only if it is finite-dimensional.

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Main Subjects


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