EVERY WEAKLY SEQUENTIALLY HYPERCYCLIC SHIFT IS NORM HYPERCYCLIC

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 2005 English Publisher:Project MUSEJournal:Mathematical Proceedings of the Royal Irish Academy, volume 105A, pages 79-85 (eissn: 2009-0021,

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Authors: Bès, Juan; Chan, Kit C.; Sanders, Rebecca;

doi: 10.1353/mpr.2005.0000 , 10.3318/pria.2005.105.2.79

EVERY WEAKLY SEQUENTIALLY HYPERCYCLIC SHIFT IS NORM HYPERCYCLIC

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Abstract

The author show that a bilateral weighted shift on \(\ell^p(\mathbb Z)\) is weakly sequentially supercyclic if and only if it is norm hypercyclic. In particular, it also follows that they are weakly sequentially hypercyclic if and only if they are hypercyclic.

Related Organizations

Bowling Green State University
United States
University System of Ohio
United States

Keywords

hypercyclicity, weak supercyclicity, norm hypercyclicity, Cyclic vectors, hypercyclic and chaotic operators, weak hypercyclicity, Canonical models for contractions and nonselfadjoint linear operators, supercyclicity

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