Journal article
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, these bounds are then shown to be optimal for general Banach spaces but not in the Hilbert space case.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, pdf, 376.0KB, Terms of use)
-
- Publisher copy:
- 10.1007/s11854-016-0039-3
Authors
- 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:
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1565-8538
- ISSN:
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0021-7670
- Keywords:
- Pubs id:
-
pubs:631745
- UUID:
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uuid:f43bdb20-4e15-42c3-b3b9-bcc35a34c512
- Local pid:
-
pubs:631745
- Source identifiers:
-
631745
- Deposit date:
-
2016-07-04
- ARK identifier:
Terms of use
- Copyright holder:
- Hebrew University Magnes Press
- Copyright date:
- 2016
- Notes:
-
This is an
accepted manuscript of a journal article published by The Hebrew University Magnes Press in Journal d'Analyse Mathématique on 2016-11-22, available online: http://dx.doi.org/10.1016/j.ultramic.2015.03.005
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