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Uniformly Continuous Functionals and M-Weakly Amenable Groups

  • Brian Forrest (a1) and Tianxuan Miao (a2)
Abstract

Let G be a locally compact group. Let AM (G) (A 0(G))denote the closure of A(G), the Fourier algebra of G in the space of bounded (completely bounded) multipliers of A(G). We call a locally compact group M-weakly amenable if AM (G) has a bounded approximate identity. We will show that when G is M-weakly amenable, the algebras AM (G) and A 0(G) have properties that are characteristic of the Fourier algebra of an amenable group. Along the way we show that the sets of topologically invariant means associated with these algebras have the same cardinality as those of the Fourier algebra.

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References
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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