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Projections In L1(G): The Unimodular Case

Journal article
Authors Mahmood Alaghmandan
Nico Spronk
Keith Taylor
Mahya Ghandehari
Published in Proceedings of the American Mathematical Society
Volume 144
Issue 11
Pages 4929-4941
ISSN 0002-9939
Publication year 2016
Published at Department of Mathematical Sciences, Analysis and Probability Theory
Pages 4929-4941
Language en
Links dx.doi.org/10.1090/proc/13142
Keywords L1-projection, locally compact group, unimodular, square-integrable representation.
Subject categories Mathematical Analysis

Abstract

We consider the issue of describing all self-adjoint idempotents (projections) in L1(G) when G is a unimodular locally compact group. The approach is to take advantage of known facts concerning subspaces of the Fourier-Stieltjes and Fourier algebras of G and the topology of the dual space of G. We obtain an explicit description of any projection in L1(G) which happens to also lie in the coefficient space of a finite direct sum of irreducible representations. This leads to a complete description of all projections in L1(G) for G belonging to a class of groups that includes SL2(R) and all second countable almost connected nilpotent locally compact groups.

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