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ARENS REGULARITY AND AMENABILITY OF LAU PRODUCT OF BANACH ALGEBRAS DEFINED BY A BANACH ALGEBRA MORPHISM

Part of: Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  31 July 2012

S. J. BHATT  and
P. A. DABHI
S. J. BHATT
Affiliation:
Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388120, Gujarat, India (email: subhashbhaib@gmail.com)
P. A. DABHI*
Affiliation:
Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388120, Gujarat, India (email: lightatinfinite@gmail.com)
*
✉For correspondence; e-mail: lightatinfinite@gmail.com
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Abstract

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Given a morphism T from a Banach algebra ℬ to a commutative Banach algebra 𝒜, a multiplication is defined on the Cartesian product space 𝒜×ℬ perturbing the coordinatewise product resulting in a new Banach algebra 𝒜×Tℬ. The Arens regularity as well as amenability (together with its various avatars) of 𝒜×Tℬ are shown to be stable with respect to T.

Keywords

perturbation of Cartesian productArens regularityamenabilityweak amenabilityapproximate amenabilityapproximate weak amenabilitycyclic amenabilityapproximate cyclic amenabilityφ-inner amenabilitycharacter amenability

MSC classification

Secondary: 46H05: General theory of topological algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 2 , April 2013 , pp. 195 - 206
Copyright
©2012 Australian Mathematical Publishing Association Inc.

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