A tauberian group algebra
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- by Peter R. Mueller-Roemer
- Proc. Amer. Math. Soc. 37 (1973), 163-166
- DOI: https://doi.org/10.1090/S0002-9939-1973-0324317-8
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Abstract:
Let G be the group of real matrices \[ (x,y) = \left ( {\begin {array}{*{20}{c}} {{e^x}} & 0 \\ y & 1 \\ \end {array} } \right )\quad (x,y \in R).\] Every proper closed two-sided ideal of ${L^1}(G)$ is contained in a maximal modular two-sided ideal. The strong radical of ${L^1}(G)$ is the set of all $f \in {L^1}(G)$ with $\smallint f(x,y)\;dy = 0$ for almost all $x \in R$. The strong structure spaces of ${L^1}(G)$ and ${L^1}(R)$ are homeomorphic.References
- Hans Reiter, Classical harmonic analysis and locally compact groups, Clarendon Press, Oxford, 1968. MR 306811
- Charles E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 115101
Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 37 (1973), 163-166
- MSC: Primary 43A20
- DOI: https://doi.org/10.1090/S0002-9939-1973-0324317-8
- MathSciNet review: 0324317