Singular-continuous unitaries and weak dynamics (Q2821814)
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scientific article; zbMATH DE number 6629394
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Singular-continuous unitaries and weak dynamics |
scientific article; zbMATH DE number 6629394 |
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Singular-continuous unitaries and weak dynamics (English)
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23 September 2016
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weakly supercyclic operators
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weakly stable operators
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unitary operators
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Hilbert spaces
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The aim of this paper is to investigate weak stability and weak supercyclicity of unitary operators on Hilbert spaces. Two questions in this direction of research are answered in the article: (1) There are singular continuous unitary operators that are weakly stable and there are singular continuous unitary operators that are weakly unstable. (2) Every weakly \(1\)-sequentially supercyclic unitary operator is singular continuous. Moreover, a sufficient condition for a weakly \(1\)-sequentially supercyclic unitary operator to be weakly stable is presented. We refer the reader to the article for unexplained terminology.
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