Commutant lifting, tensor algebras, and functional calculus (Q2747929)
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scientific article; zbMATH DE number 1658545
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Commutant lifting, tensor algebras, and functional calculus |
scientific article; zbMATH DE number 1658545 |
Statements
23 May 2002
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non-commutative multivariable operator theory
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commutant lifting theorem
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interpolation
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non-commutative Poisson transform
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von Neumann inequality
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tensor algebras
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functional calculus
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contractive sequences of operators
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Commutant lifting, tensor algebras, and functional calculus (English)
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The author continues his study of non-commutative, multivariable operator theory, by obtaining in this paper the analogue of Parrott's generalization of Sz-Nagy-Foias commutant lifting theorem. This result implies Tomita-type commutant results and several interpolation theorems. NEWLINENEWLINENEWLINEA variant of the non-commutative Poisson transform is used to extend the von Neumann inequality to tensor algebras, and to provide a generalization of the functional calculus for contractive sequences of operators on Hilbert space. Commutative versions of these results are also considered.
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