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Super-Ergodic operators

Author: M. Yahdi
Journal: Proc. Amer. Math. Soc. 134 (2006), 2613-2620
MSC (2000): Primary 47A35, 46B08; Secondary 47B07, 47B99
Published electronically: February 17, 2006
MathSciNet review: 2213740
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Abstract: The aim of this work is to study operators naturally connected to Ergodic operators in infinite-dimensional Banach spaces, such as Uniform-Ergodic, Cesaro-bounded and Power-bounded operators, as well as stable and superstable operators. In particular, super-Ergodic operators are introduced and shown to be strictly between Ergodic and Uniform-Ergodic operators, and that any power bounded operator is super-Ergodic in a superreflexive space. New relationships between these operators are shown, others are proven to be optimal or can be ameliorated according to structural properties of the Banach space, such as the superreflexivity or with unconditional basis.

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Additional Information

M. Yahdi
Affiliation: Department of Mathematics and Computer Science, Ursinus College, Collegeville, Pennsylvania 19426

Keywords: Super-Ergodic, Ergodic operator, stable operator, Banach space, ultrapower
Received by editor(s): March 11, 2005
Received by editor(s) in revised form: March 23, 2005
Published electronically: February 17, 2006
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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