Analytic perturbation of the Taylor spectrum

Author:
Zbigniew Slodkowski

Journal:
Trans. Amer. Math. Soc. **297** (1986), 319-336

MSC:
Primary 47A56; Secondary 32A99, 47A10, 47D99

DOI:
https://doi.org/10.1090/S0002-9947-1986-0849482-9

MathSciNet review:
849482

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Abstract | References | Similar Articles | Additional Information

Abstract: Let , , be analytic families of bounded operators in a complex Banach space , such that for each the operators and , , commute. Main result: If denotes the Taylor spectrum of the tuple , then the set-valued function is analytic. Analyticity of such set-valued functions is defined here by a simultaneous local maximum property of -tuples of complex polynomials on the graph of .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1986-0849482-9

Keywords:
Analytic multifunction,
local maximum property,
joint spectrum,
Taylor spectrum,
exact complex,
analytic perturbation

Article copyright:
© Copyright 1986
American Mathematical Society