A characterization of a class of [Z] groups via Korovkin theory |
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| Authors: | Manju Rani Agrawal U. B. Tewari |
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| Affiliation: | (1) Mathematical Sciences Division, Institute of Advanced Study in Science and Technology, Khanapara, 781022 Guwahati, India;(2) Department of Mathematics, Indian Institute of Technology, 208016 Kanpur, India |
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| Abstract: | We characterize all the central topological groupsG for which the centreZ(L 1(G)) of the group algebra admits a finite universal Korovkin set. It is proved thatZ(L 1(G)) has a finite universal Korovkin set iffĜ is a finite dimensional, separable metric space. This is equivalent to the fact thatG is separable, metrizable andG/K has finite torsion free rank, whereK is a compact open normal subgroup of certain direct summand ofG. |
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| Keywords: | KeywordHeading" > and phrases Universal Korovkin set central topological group continuous irreducible unitary representation induced representation centre of group algebra Segal algebra |
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