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On the set of topologically invariant means on an algebra of convolution operators on

Authors:	Edmond E Granirer

Institution:	Department of Mathematics, The University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z2

Abstract:	Let be a locally compact group, $A_{p}=A_{p}(G)$ the Banach algebra defined by Herz; thus $A_{2}(G)=A(G)$ is the Fourier algebra of . Let $PM_{p}=A^{}_{p}$ the dual, $J \subset A_{p}$ a closed ideal, with zero set , and $\mathbb {P} = (A_{p}/J)^{}$ . We consider the set $TIM_{\mathbb {P}}(x) \subset {\mathbb {P}}^{}$ of topologically invariant means on $\mathbb {P}$ at $x\in F$ , where is ``thin.' We show that in certain cases card $TIM_{\mathbb {P}}(x) \geq 2^{c}$ and $TIM_{\mathbb {P}}(x)$ does not have the WRNP, i.e. is far from being weakly compact in $\mathbb {P}^{}$ . This implies the non-Arens regularity of the algebra $A_{p}/J$ .

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