Some improvements of the Katznelson-Tzafriri theorem on Hilbert space
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.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2014
- DOI:
- 10.48550/arXiv.1410.1294
- arXiv:
- arXiv:1410.1294
- Bibcode:
- 2014arXiv1410.1294S
- Keywords:
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- Mathematics - Functional Analysis
- E-Print:
- 13 pages, to appear in Proceedings of the American Mathematical Society