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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Central approximate units in a certain ideal of $ L\sp{1}(G)$


Authors: Ernst Kotzmann and Harald Rindler
Journal: Proc. Amer. Math. Soc. 57 (1976), 155-158
MSC: Primary 43A20; Secondary 22D15
DOI: https://doi.org/10.1090/S0002-9939-1976-0404988-0
MathSciNet review: 0404988
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Abstract: In this paper we show that for a locally compact group $ G$ the ideal $ {L^0}(G) = \{ f\vert f \in {L^1}(G),\smallint f = 0\} $ of $ {L^1}(G)$ has multiple approximate units belonging to the center of $ {L^0}(G)$ iff $ G$ has a basis of invariant neighbourhoods of 1 and if all conjugacy classes of $ G$ are precompact, or, equivalently, the group of inner automorphisms is precompact in the group of all topological automorphisms. In a sense this is part of the problem to characterize certain classes of groups by properties of the group algebra.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0404988-0
Keywords: Locally compact group, group algebra, convolution, center of an algebra, central function, approximate unit, compact invariant neighbourhood, amenable group, precompact conjugacy class
Article copyright: © Copyright 1976 American Mathematical Society

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