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Some improvements of the Katznelson- Tzafriri theorem on Hilbert space


Author: David Seifert
Journal: Proc. Amer. Math. Soc. 143 (2015), 3827-3838
MSC (2010): Primary 47D03; Secondary 43A45, 43A46, 47A35
DOI: https://doi.org/10.1090/proc/12323
Published electronically: May 22, 2015
MathSciNet review: 3359574
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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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Additional Information

David Seifert
Affiliation: Mathematical Institute, 24–29 St Giles’, OxfordOX1 3LB, United Kingdom
Address at time of publication: St. John’s College, St. Giles, Oxford, OX1 3JP, United Kingdom
Email: david.seifert@sjc.ox.ac.uk

DOI: https://doi.org/10.1090/proc/12323
Received by editor(s): March 27, 2013
Received by editor(s) in revised form: July 17, 2013
Published electronically: May 22, 2015
Communicated by: Pamela B. Gorkin
Article copyright: © Copyright 2015 American Mathematical Society