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Proceedings of the American Mathematical Society
Vol. 134, No. 9 (Sep., 2006), pp. 2613-2620
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/4098110
Page Count: 8
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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.
Proceedings of the American Mathematical Society © 2006 American Mathematical Society