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2011 Supercyclicity and Hypercyclicity of an Isometry Plus a Nilpotent
S. Yarmahmoodi, K. Hedayatian, B. Yousefi
Abstr. Appl. Anal. 2011: 1-11 (2011). DOI: 10.1155/2011/686832


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.


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S. Yarmahmoodi. K. Hedayatian. B. Yousefi. "Supercyclicity and Hypercyclicity of an Isometry Plus a Nilpotent." Abstr. Appl. Anal. 2011 1 - 11, 2011.


Published: 2011
First available in Project Euclid: 12 August 2011

zbMATH: 1221.47021
MathSciNet: MR2800079
Digital Object Identifier: 10.1155/2011/686832

Rights: Copyright © 2011 Hindawi

Vol.2011 • 2011
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