Zeros of Fredholm operator valued \(H^p\)-functions (Q2747570)
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scientific article; zbMATH DE number 1658046
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Zeros of Fredholm operator valued \(H^p\)-functions |
scientific article; zbMATH DE number 1658046 |
Statements
4 September 2002
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Fatou's theorem
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Radon-Nikodym property
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quasi-Banach operator ideals
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Blaschke product
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Fredholm operators
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traces
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determinants
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Zeros of Fredholm operator valued \(H^p\)-functions (English)
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This paper deals with operator \(H^p\)-functions of the form NEWLINE\[NEWLINE T(z) := I+A(z), \;\;z\in D, NEWLINE\]NEWLINE where \(D\) is the unite disc and \(A(z)\) is a compact, linear and bounded operator on a Banach space. Sufficient conditions are presented which guarantee that Fatou's theorem is valid. Using the theory of traces and determinants on quasi-Banach operator ideals, the author develops conditions that guarantee that the zeros of Fredholm operator valued \(H^p\)-functions satisfy the Blaschke condition.
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