Central approximate units in a certain ideal of $L^{1}(G)$
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- by Ernst Kotzmann and Harald Rindler PDF
- Proc. Amer. Math. Soc. 57 (1976), 155-158 Request permission
Abstract:
In this paper we show that for a locally compact group $G$ the ideal ${L^0}(G) = \{ f|f \in {L^1}(G),\smallint f = 0\}$ 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.References
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Additional Information
- © Copyright 1976 American Mathematical Society
- 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