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Weak amenability of Segal algebras

Authors: H. G. Dales and S. S. Pandey
Journal: Proc. Amer. Math. Soc. 128 (2000), 1419-1425
MSC (1991): Primary 46J10
Published electronically: October 6, 1999
MathSciNet review: 1641681
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Abstract: Let $G$ be a locally compact abelian group, and let $p \in [1,\infty)$. We show that the Segal algebra $S_p(G)$ is always weakly amenable, but that it is amenable only if $G$ is discrete.

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Additional Information

H. G. Dales
Affiliation: Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, England

S. S. Pandey
Affiliation: Department of Mathematics, R. D. University, Jabalpur, India

Received by editor(s): March 10, 1998
Received by editor(s) in revised form: July 3, 1998
Published electronically: October 6, 1999
Additional Notes: The second author acknowledges with thanks the support of the Royal Society-INSA exchange program which enabled him to visit the University of Leeds to work with the first author. He is also thankful to the Department of Pure Mathematics at Leeds for hospitality.
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2000 American Mathematical Society