Abstract
We prove that if $T$ is a power-bounded operator of class $C_{*\cdot}$ on a Hilbert space which commutes with a nonzero quasinilpotent operator, then $T$ has a nontrivial invariant subspace. Connections with the questions of convergence of $T^n$ to $0$ in the strong operator topology and of cyclicity of power-bounded operators of class $C_{1\cdot}$ are discussed.
Citation
L´aszl´o K´erchy. Quoc Phong Vu. "ON INVARIANT SUBSPACES FOR POWER-BOUNDED OPERATORS OF CLASS $C_{1\cdot}$." Taiwanese J. Math. 7 (1) 69 - 75, 2003. https://doi.org/10.11650/twjm/1500407517
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