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Rates of decay in the classical Katznelson-Tzafriri theorem

Abstract:

The Katznelson-Tzafriri Theorem states that, given a powerbounded operator T , T n(I − T ) → 0 as n → ∞ if and only if the spectrum σ(T ) of T intersects the unit circle T in at most the point 1. This paper investigates the rate at which decay takes place when σ(T ) ∩ T = {1}. The results obtained lead, in particular, to both upper and lower bounds on this rate of decay in terms of the growth of the resolvent operator R(eiθ , T ) as θ → 0. In the special case of polynomial resolvent growth, t...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s11854-016-0039-3

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Institution:
University of Oxford
Department:
Oxford
Role:
Author
Publisher:
Hebrew University Magnes Press
Journal:
Journal d'Analyse Mathematique More from this journal
Volume:
130
Issue:
1
Pages:
329–354
Publication date:
2016-11-22
Acceptance date:
2014-03-02
DOI:
EISSN:
1565-8538
ISSN:
0021-7670
Keywords:
Pubs id:
pubs:631745
UUID:
uuid:f43bdb20-4e15-42c3-b3b9-bcc35a34c512
Local pid:
pubs:631745
Source identifiers:
631745
Deposit date:
2016-07-04

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