Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the set of topologically invariant means on an algebra of convolution operators on $L^{p}(G)$


Author: Edmond E. Granirer
Journal: Proc. Amer. Math. Soc. 124 (1996), 3399-3406
MSC (1991): Primary 43A22, 42B15, 22D15; Secondary 42A45, 43A07, 44A35, 22D25
Erratum: Proc. Amer. Math. Soc. (recently posted)
MathSciNet review: 1340388
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 ``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 $A_{p}/J$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 43A22, 42B15, 22D15, 42A45, 43A07, 44A35, 22D25

Retrieve articles in all journals with MSC (1991): 43A22, 42B15, 22D15, 42A45, 43A07, 44A35, 22D25


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

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03444-2
PII: S 0002-9939(96)03444-2
Received by editor(s): March 13, 1995
Received by editor(s) in revised form: May 8, 1995
Communicated by: Dale E. Alspach
Article copyright: © Copyright 1996 American Mathematical Society