Second cohomology group of group algebras with coefficients in iterated duals

Author:
A. Pourabbas

Journal:
Proc. Amer. Math. Soc. **132** (2004), 1403-1410

MSC (2000):
Primary 43A20; Secondary 46M20

Published electronically:
August 28, 2003

MathSciNet review:
2053346

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we show that the first cohomology group is zero for every odd and for every -set . In the case when is a discrete group, this is a generalization of the following result of Dales et al.: for any locally compact group , is -weakly amenable.

Next we show that the second cohomology group is a Banach space. Finally, for every locally compact group we show that is a Banach space for every odd .

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Additional Information

**A. Pourabbas**

Affiliation:
Faculty of Mathematics and Computer Science, Amirkabir University, 424 Hafez Avenue, Tehran 15914, Iran

Email:
arpabbas@aut.ac.ir

DOI:
https://doi.org/10.1090/S0002-9939-03-07219-8

Received by editor(s):
January 14, 2002

Received by editor(s) in revised form:
December 31, 2002

Published electronically:
August 28, 2003

Additional Notes:
This research was supported by a grant from Amir Kabir University. The author would like thank the Institute for their kind support.

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2003
American Mathematical Society