A Katznelson-Tzafriri type theorem in Hilbert spaces

Léka, Zoltán

doi:10.1090/S0002-9939-09-09939-0

A Katznelson-Tzafriri type theorem in Hilbert spaces
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by Zoltán Léka PDF

Proc. Amer. Math. Soc. 137 (2009), 3763-3768 Request permission

Abstract:

Our aim is to characterize, via an ergodic condition, the norm convergence $\lim _{n \rightarrow \infty } \|T^nQ\| = 0$ when $T$ is a power-bounded operator on a Hilbert space and $Q$ commutes with $T.$ We shall also prove that if $f \in A^+(\mathbb {T})$ and $Q = f(T),$ the given condition is equivalent to the vanishing of $f$ on the peripheral spectrum of $T.$

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