On the set of topologically invariant means on an algebra of convolution operators on $L^p(G)$
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- by Edmond E. Granirer PDF
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Erratum: Proc. Amer. Math. Soc. 129 (2001), 2503-2503.
Abstract:
Let $G$ 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 $G$. Let $PM_{p}=A^{*}_{p}$ the dual, $J \subset A_{p}$ a closed ideal, with zero set $F=Z(J)$, 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 $F$ is âthin.â 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 $A_{p}/J$.References
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Additional Information
- Edmond E. Granirer
- Affiliation: Department of Mathematics, The University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z2
- Email: granirer@math.ubc.ca
- Received by editor(s): March 13, 1995
- Received by editor(s) in revised form: May 8, 1995
- Communicated by: Dale E. Alspach
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 3399-3406
- MSC (1991): Primary 43A22, 42B15, 22D15; Secondary 42A45, 43A07, 44A35, 22D25
- DOI: https://doi.org/10.1090/S0002-9939-96-03444-2
- MathSciNet review: 1340388