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Proceedings of the American Mathematical Society

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A tauberian group algebra


Author: Peter R. Mueller-Roemer
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
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Abstract: Let G be the group of real matrices

$\displaystyle (x,y) = \left( {\begin{array}{*{20}{c}} {{e^x}} & 0 \\ y & 1 \\ \end{array} } \right)\quad (x,y \in R).$

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 [Enhancements On Off] (What's this?)

  • [1] H. Reiter, Classical harmonic analysis and locally compact groups, Oxford Univ. Press, Oxford, 1968. MR 0306811 (46:5933)
  • [2] C. E. Rickart, General theory of Banach algebras, University Series in Higher Math., Van Nostrand, Princeton, N.J., 1960. MR 22 #5903. MR 0115101 (22:5903)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0324317-8
Keywords: Tauberian, completely regular algebra, strong radical, group algebra, amenable group
Article copyright: © Copyright 1973 American Mathematical Society

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