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Completely continuous elements of Banach algebras related to locally compact groups

Published online by Cambridge University Press:  17 April 2009

M. J. Mehdipour  and
R. Nasr-Isfahani
M. J. Mehdipour
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156–83111, Iran, e-mail: isfahani@cc.iut.ac.ir
R. Nasr-Isfahani
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156–83111, Iran, e-mail: isfahani@cc.iut.ac.ir
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Let G be a locally compact group and be the Banach space of all essentially bounded measurable functions on G vansihing an infinity. Here, we study some families of right completely continuous elements in the Banach algebra equipped with an Arens type product. As the main result, we show that has a certain right completely continuous element if and only if G is compact.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 76 , Issue 1 , August 2007 , pp. 49 - 54
Copyright
Copyright © Australian Mathematical Society 2007

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