On contractions without disjoint invariant subspaces

Takahashi, Katsutoshi

doi:10.1090/S0002-9939-1990-1028296-X

On contractions without disjoint invariant subspaces
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by Katsutoshi Takahashi PDF

Proc. Amer. Math. Soc. 110 (1990), 935-937 Request permission

Abstract:

Assume $T$ is a contraction with the following property: there exists an operator $X$ with dense range such that $XT = WX$ where $W$ is a bilateral shift. We give a necessary and sufficient condition that $T$ has no disjoint invariant subspaces.

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