Supercyclicity and Hypercyclicity of an Isometry Plus a Nilpotent

Suppose that X is a separable normed space and the operators A and Q are bounded on X. In this paper, it is shown that if AQ=QA, A is an isometry, and Q is a nilpotent then the operator A+Q is neither supercyclic nor weakly hypercyclic. Moreover, if the underlying space is a Hilbert space and A is a...

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Bibliographic Details
Published in:Abstract and applied analysis 2011, Vol.2011 (2011), p.1-11
Main Authors: Yarmahmoodi, S., Hedayatian, Karim, Yousefi, Bahmann
Format: Article
Language:English
Online Access:Get full text
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Summary:Suppose that X is a separable normed space and the operators A and Q are bounded on X. In this paper, it is shown that if AQ=QA, A is an isometry, and Q is a nilpotent then the operator A+Q is neither supercyclic nor weakly hypercyclic. Moreover, if the underlying space is a Hilbert space and A is a co-isometric operator, then we give sufficient conditions under which the operator A+Q satisfies the supercyclicity criterion.
ISSN:1085-3375
1687-0409