Ergodic characterizations of reflexivity of Banach spaces

Vladimir P. Fonf, Michael Lin, Przemyslaw Wojtaszczyk

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

Abstract

Let X be a Banach space with a basis. We prove the following characterizations: (i) X is finite-dimensional if and only if every power-bounded operator is uniformly ergodic. (ii) X is reflexive if and only if every power-bounded operator is mean ergodic. (iii) X is quasi-reflexive of order one if and only if for every power-bounded operator T, T or T* is mean ergodic.

Original languageEnglish
Pages (from-to)146-162
Number of pages17
JournalJournal of Functional Analysis
Volume187
Issue number1
DOIs
StatePublished - 1 Dec 2001

ASJC Scopus subject areas

  • Analysis

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