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Invariant Subspaces for Algebras of Linear Operators and Amenable Locally Compact Groups
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 …