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Ergodic Characterizations of Reflexivity of Banach Spaces

✍ Scribed by Vladimir P. Fonf; Michael Lin; Przemyslaw Wojtaszczyk

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 308 KB
Volume: 187
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2001.3806

No coin nor oath required. For personal study only.

✦ Synopsis

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 g is mean ergodic.

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