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

Author:
Edmond E. Granirer

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

Erratum:
Proc. Amer. Math. Soc. (recently posted)

MathSciNet review:
1340388

Full-text PDF

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Abstract: Let be a locally compact group, the Banach algebra defined by Herz; thus is the Fourier algebra of . Let the dual, a closed ideal, with zero set , and . We consider the set of topologically invariant means on at , where is ``thin.'' We show that in certain cases card and does not have the WRNP, i.e. is far from being weakly compact in . This implies the non-Arens regularity of the algebra .

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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

DOI:
https://doi.org/10.1090/S0002-9939-96-03444-2

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