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

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 under...

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Published in:arXiv.org 2023-02
Main Authors: rest, Brian, Sawatzky, John, Thamizhazhagan, Aasaimani
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description 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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title Arens regularity of ideals in \(A(G)\), \(A_{cb}(G)\) and \(A_M(G)\)
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