Invariant subspaces for algebras of linear operators and amenable locally compact groups
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- by Anthony T. M. Lau and James C. S. Wong PDF
- Proc. Amer. Math. Soc. 102 (1988), 581-586 Request permission
Abstract:
Let $G$ be a locally compact group. We prove in this paper that $G$ is amenable if and only if the group algebra ${L_1}\left ( G \right )$ (respectively the measure algebra $M\left ( G \right )$) satisfies a finite-dimensional invariant subspace property $T\left ( n \right )$ for $n$-dimensional subspaces contained in a subset $X$ of a separated locally convex space $E$ when ${L_1}\left ( G \right )$ (respectively $M\left ( G \right )$) is represented as continuous linear operators on $E$. We also prove that for any locally compact group, the Fourier algebra $A\left ( G \right )$ and the Fourier Stieltjes algebra $B\left ( G \right )$ always satisfy $T\left ( n \right )$ for each $n = 1,2, \ldots$.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 102 (1988), 581-586
- MSC: Primary 43A20; Secondary 47D05
- DOI: https://doi.org/10.1090/S0002-9939-1988-0928984-8
- MathSciNet review: 928984