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ARENS PRODUCTS, ARENS REGULARITY AND RELATED PROBLEMS

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

Published online by Cambridge University Press:  04 December 2019

RUKI MATSUI Open the ORCID record for RUKI MATSUI [Opens in a new window]  and
YUJI TAKAHASHI Open the ORCID record for YUJI TAKAHASHI [Opens in a new window]
RUKI MATSUI
Affiliation:
Department of Mathematics,Hokkaido University of Education, Asahikawa, 070-8621, Japan email [email protected]
YUJI TAKAHASHI*
Affiliation:
Department of Mathematics,Hokkaido University of Education, Asahikawa, 070-8621, Japan email [email protected]
*
✉[email protected]
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Abstract

We study the second dual algebra of a Banach algebra and related problems. We resolve some questions raised by Ülger, which are related to Arens products. We then discuss a question of Gulick on the radical of the second dual algebra of the group algebra of a discrete abelian group and give an application of Arens regularity to Fourier and Fourier–Stieltjes transforms.

Keywords

Arens productArens regularitysecond dual Banach algebraradicallocally compact groupgroup algebrameasure algebraC∗ -algebraFourier and Fourier–Stieltjes transforms

MSC classification

Primary: 43A20: $L^1$-algebras on groups, semigroups, etc.
Secondary: 46H05: General theory of topological algebras 46L05: General theory of $C^*$-algebras 43A25: Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 102 , Issue 1 , August 2020 , pp. 138 - 150
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Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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