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New Deformations of Convolution Algebras and Fourier Algebras on Locally Compact Groups

Published:2016-09-23
Printed: Apr 2017
• Hun Hee Lee,
Department of Mathematical Sciences, Seoul National University, San56-1 Shinrim-dong Kwanak-gu, Seoul 151-747, Republic of Korea
• Sang-gyun Youn,
Department of Mathematical Sciences, Seoul National University, San56-1 Shinrim-dong Kwanak-gu, Seoul 151-747, Republic of Korea
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Abstract

In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on locally compact groups. We demonstrate that this new deformation allows us to reveal some information of the underlying groups by examining Banach algebra properties of deformed algebras. More precisely, we focus on representability as an operator algebra of deformed convolution algebras on compact connected Lie groups with connection to the real dimension of the underlying group. Similarly, we investigate complete representability as an operator algebra of deformed Fourier algebras on some finitely generated discrete groups with connection to the growth rate of the group.
 Keywords: Fourier algebra, convolution algebra, operator algebra, Beurling algebra
 MSC Classifications: 43A20 - $L^1$-algebras on groups, semigroups, etc. 43A30 - Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. 47L30 - Abstract operator algebras on Hilbert spaces 47L25 - Operator spaces (= matricially normed spaces) [See also 46L07]

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