Supercyclicity and Hypercyclicity of an Isometry Plus a Nilpotent

S. Yarmahmoodi, K. Hedayatian and B. Yousefi

Abstract and Applied Analysis, 2011, vol. 2011, issue 1

Abstract: 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.

Date: 2011
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https://doi.org/10.1155/2011/686832

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:686832

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