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ON HOMOLOGICAL PROPERTIES FOR SOME MODULES OF UNIFORMLY CONTINUOUS FUNCTIONS OVER CONVOLUTION ALGEBRAS

Part of: Topological algebras, normed rings and algebras, Banach algebras Abstract harmonic analysis

Published online by Cambridge University Press:  13 July 2011

RASOUL NASR-ISFAHANI  and
SIMA SOLTANI RENANI
RASOUL NASR-ISFAHANI*
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran (email: [email protected])
SIMA SOLTANI RENANI
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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For a locally compact group G, let LUC(G) denote the space of all left uniformly continuous functions on G. Here, we investigate projectivity, injectivity and flatness of LUC(G) and its dual space LUC(G)* as Banach left modules over the group algebra as well as the measure algebra of G.

Keywords

amenabilityflatnessinjectivityprojectivityBanach modulelocally compact group

MSC classification

Secondary: 43A07: Means on groups, semigroups, etc.; amenable groups 43A20: $L^1$-algebras on groups, semigroups, etc. 46H05: General theory of topological algebras 46H25: Normed modules and Banach modules, topological modules (if not placed in or )
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 2 , October 2011 , pp. 177 - 185
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

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