Dissipative operators on quotient spaces of \(H^ 2\) (Q2367639)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Dissipative operators on quotient spaces of \(H^ 2\) |
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Dissipative operators on quotient spaces of \(H^ 2\) (English)
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19 August 1993
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For an inner function \(\varphi\) on the unit disc \(D\), let \(A(\varphi)\) denote the commutant of the compression of the standard unilateral shift onto \(H^ 2/ \varphi H^ 2\). In this paper the author finds necessary and sufficient conditions for an operator in \(A(\varphi)\) to be dissipative. Also, for a singular inner function \(\varphi\), sufficient conditions for the Cayley transform of a constant multiple of a dissipative operator in \(A(\varphi)\) to be noncyclic and to belong to the class \(C_ 0\) of Sz.-Nagy and Foias are given.
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Cayley transformation
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inner function
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Cayley transform
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dissipative operator
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class \(C_ 0\) of Sz.-Nagy and Foias
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