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Some developments around the Katznelson-Tzafriri theorem

Abstract:
This paper is a survey article on developments arising from a theorem proved by Katznelson and Tzafriri in 1986 showing that lim𝑛→∞||𝑇𝑛(𝐼−𝑇)||=0limn→∞||Tn(I−T)||=0 if T is a power-bounded operator on a Banach space and σ(𝑇)∩𝕋⊆{1}σ(T)∩T⊆{1}. Many variations and consequences of the original theorem have been proved subsequently, and we provide an account of this branch of operator theory.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s44146-022-00006-1

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Springer
Journal:
Acta Scientiarum Mathematicarum More from this journal
Volume:
88
Issue:
1-2
Pages:
53-84
Publication date:
2022-09-02
Acceptance date:
2022-03-01
DOI:
EISSN:
2064-8316
ISSN:
0001-6969
Language:
English
Keywords:
Pubs id:
1249019
Local pid:
pubs:1249019
Deposit date:
2022-03-31

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