New Deformations of Convolution Algebras and Fourier Algebras on Locally Compact Groups
Printed: Apr 2017
Hun Hee Lee,
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.
Fourier algebra, convolution algebra, operator algebra, Beurling algebra
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]