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2009 | 193 | 1 | 53-78
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On character amenable Banach algebras

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We obtain characterizations of left character amenable Banach algebras in terms of the existence of left ϕ-approximate diagonals and left ϕ-virtual diagonals. We introduce the left character amenability constant and find this constant for some Banach algebras. For all locally compact groups G, we show that the Fourier-Stieltjes algebra B(G) is C-character amenable with C < 2 if and only if G is compact. We prove that if A is a character amenable, reflexive, commutative Banach algebra, then A ≅ ℂⁿ for some n ∈ ℕ. We show that the left character amenability of the double dual of a Banach algebra A implies the left character amenability of A, but the converse statement is not true in general. In fact, we give characterizations of character amenability of L¹(G)** and A(G)**. We show that a natural uniform algebra on a compact space X is character amenable if and only if X is the Choquet boundary of the algebra. We also introduce and study character contractibility of Banach algebras.
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  • Department of Mathematics and Statistics, University of Windsor, Windsor, ON, Canada N9B 3P4
  • Department of Mathematics and Statistics, University of Windsor, Windsor, ON, Canada N9B 3P4
autor
  • Department of Mathematics and Statistics, University of Windsor, Windsor, ON, Canada N9B 3P4
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bwmeta1.element.bwnjournal-article-doi-10_4064-sm193-1-3
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