SPECTRAL INVARIANCE AND THE HOLOMORPHIC FUNCTIONAL CALCULUS OF J.L. TAYLOR IN Ψ-ALGEBRAS

If X is a Hilbert space it is shown that very general subalgebras A of L(X) contain the holomorphic functional calculus in several variables in the sense of J.L. Taylor. In particular, Taylor's holomorphic functional calculus applies to Ψ*-algebras (cf. [12], Definition 5.1), and so gives a use...

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Bibliographic Details
Published in:Journal of operator theory 1994-10, Vol.32 (2), p.311-329
Main Author: LAUTER, ROBERT
Format: Article
Language:English
Subjects:
Algebra
Algebraic topology
Banach space
Commuting
Hilbert calculus
Hilbert spaces
Mathematical theorems
Mathematics
Operator theory
Subalgebras
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Summary:If X is a Hilbert space it is shown that very general subalgebras A of L(X) contain the holomorphic functional calculus in several variables in the sense of J.L. Taylor. In particular, Taylor's holomorphic functional calculus applies to Ψ*-algebras (cf. [12], Definition 5.1), and so gives a useful tool for the investigation of certain algebras of pseudo-differential operators and of Fréchet operator algebras on singular spaces. Taylor's holomorphic functional calculus applies also to algebras of n × n-matrices with elements in Ψ*-algebras and even more general algebras. Furthermore, an example shows that Taylor's holomorphic functional calculus for at least three commuting operators on a Hilbert space is, in general, richer than any other multidimensional holomorphic functional calculus in commutative subalgebras of L(X).
ISSN:0379-4024
1841-7744