Quasianalytic contractions and function algebras (Q2884640)
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scientific article; zbMATH DE number 6039325
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quasianalytic contractions and function algebras |
scientific article; zbMATH DE number 6039325 |
Statements
Quasianalytic contractions and function algebras (English)
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30 May 2012
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commutant
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hyperinvariant subspace
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functional calculus
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quasianalyticity
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Doulgas algebra
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cyclic \(C_{10}\)-contractions
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Extending his previous results in [Indiana Univ. Math. J. 38, No. 1, 173--188 (1989; Zbl 0693.47014)], the author proves spectral mapping theorems for the residual set and the quasianalytic spectral set. Further, the hyperinvariant subspace problem (HSP) in the class \(L_0(H)\) is shown to be strongly related to (HSP) in the subclass \(L_1(H)\) of \(L_0(H)\). For an operator \(T\) in the class \(L_1(H)\), the functional commutant algebra \(F(T)\) is proven to be quasianalytic and the spectral relations are described. Furthermore, for any contraction \(T\in L_1(H)\), some sufficient and necessary conditions for \(F(T)\) to be a Douglas algebra are given.
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