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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2006; 43(6): 1219-1229

Printed November 1, 2006

Copyright © The Korean Mathematical Society.

On the hereditarily hypercyclic operators

Bahman Yousefi and Ali Farrokhinia

Shiraz University, Tarbiat Modares University

Abstract

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Let $X$ be a separable Banach space. We give sufficient conditions under which $T:X \rightarrow X$ is hereditarily hypercyclic. Also, we prove that hereditarily hypercyclicity with respect to a special sequence implies the hereditarily hypercyclicity with respect to the entire sequence.

Keywords: hereditarily hpercyclicity, hypercyclicity criterion

MSC numbers: 47A16, 47L10

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