On the Taylor functional calculus (Q2773430)
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scientific article; zbMATH DE number 1710020
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Taylor functional calculus |
scientific article; zbMATH DE number 1710020 |
Statements
On the Taylor functional calculus (English)
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21 February 2002
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Taylor's functional calculus
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Taylor spectrum
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Martinelly-Vasilescu type formula
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superposition property
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spectral mapping theorem
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0.8945147
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0.8911288
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Let \(A=(A_1, \dots, A_n)\) be an \(n\)-tuple of mutually commuting operators acting on a Banach space. It is pointed out that the known representation of \(f(A)\) for \(f\) analytic on a neighbourhood of the Taylor spectrum of \(A\) is rather complicated. In this connection the author gives a new Martinelly-Vasilescu type formula for \(f(A)\) and uses it to obtain simple proofs of basic properties of the Taylor functional calculus, such as the superposition property and the spectral mapping theorem.
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