On the orbit of an \(A\)-\(m\)-isometry (Q2860925)
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scientific article; zbMATH DE number 6225533
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the orbit of an \(A\)-\(m\)-isometry |
scientific article; zbMATH DE number 6225533 |
Statements
11 November 2013
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\(A\)-\(m\)-isometry
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semi-inner products
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supercyclic operators
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hypercyclic operators
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invariant set
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On the orbit of an \(A\)-\(m\)-isometry (English)
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Let \(H\) be a Hilbert space and \(A\) a positive semi-definite operator on \(H\). A bounded linear operator \(T\) on \(H\) is an \(A\)-\(m\)-isometry if it satisfies the identity NEWLINE\[NEWLINE \sum_{k=0}^{m} (-1)^{m-k}{m \choose k}T^{*k}AT^k=0.NEWLINE\]NEWLINE In this paper, supercyclicity and hypercyclicity of \(A\)-\(m\)-isometries are studied. Similar results are obtained as those proved by \textit{T. Bermúdez} et al. [Integral Equations Oper. Theory 64, No. 4, 487--494 (2009; Zbl 1196.47007)] and \textit{M. F. Ahmadi} and \textit{K. Hedayatian} [Rocky Mt. J. Math. 42, No. 1, 15--23 (2012; Zbl 1258.47011)] for \(m\)-isometries.
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