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COMPACT LEFT MULTIPLIERS ON BANACH ALGEBRAS RELATED TO LOCALLY COMPACT GROUPS

Part of: Topological algebras, normed rings and algebras, Banach algebras Special classes of linear operators Abstract harmonic analysis

Published online by Cambridge University Press:  13 March 2009

M. J. MEHDIPOUR  and
R. NASR-ISFAHANI
M. J. MEHDIPOUR
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran (email: [email protected])
R. NASR-ISFAHANI*
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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We deal with the dual Banach algebras for a locally compact group G. We investigate compact left multipliers on , and prove that the existence of a compact left multiplier on is equivalent to compactness of G. We also describe some classes of left completely continuous elements in .

Keywords

Arens productcompact operatorleft completely continuous elementleft multiplierlocally compact group

MSC classification

Secondary: 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc. 46H05: General theory of topological algebras 47B48: Operators on Banach algebras 47B07: Operators defined by compactness properties
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 2 , April 2009 , pp. 227 - 238
Copyright
Copyright © Australian Mathematical Society 2009

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