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
Abstract | References | Similar Articles | Additional Information
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