IM PAN
INSTYTUT MATEMATYCZNY · POLSKA AKADEMIA NAUK
STUDIA MATHEMATICA
ISSN: 0039-3223(p) 1730-6337(e)
 

On character amenable Banach algebras
Z. Hu1, M. Sangani Monfared2, T. Traynor3
Studia Math. 193 (2009), 53-78
doi:10.4064/sm193-1-3
Abstract: We obtain characterizations of left character amenable Banach algebras in terms of the existence of left $\phi$-approximate diagonals and left $\phi$-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 $A\cong \mathbb C^n$ for some $n\in \mathbb N$. 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 $L^1(G)^{**}$ 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.

MSC (2010): 22D15, 43A20, 43A30, 43A40, 46H20, 46H25.
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  1. Department of Mathematics and Statistics
    University of Windsor
    Windsor, ON, Canada N9B 3P4
  2. Department of Mathematics and Statistics
    University of Windsor
    Windsor, ON, Canada N9B 3P4
  3. Department of Mathematics and Statistics
    University of Windsor
    Windsor, ON, Canada N9B 3P4