Some improvements of the Katznelson- Tzafriri theorem on Hilbert space

Seifert, David

doi:10.1090/proc/12323

Some improvements of the Katznelson- Tzafriri theorem on Hilbert space
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Proc. Amer. Math. Soc. 143 (2015), 3827-3838 Request permission

Abstract:

This paper extends two recent improvements in the Hilbert space setting of the well-known Katznelson-Tzafriri theorem by establishing both a version of the result valid for bounded representations of a large class of abelian semigroups and a quantified version for contractive representations. The paper concludes with an outline of an improved version of the Katznelson-Tzafriri theorem for individual orbits, whose validity extends even to certain unbounded representations.

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