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Zbl 1052.47009
Andersson, Mats
(Ultra)differentiable functional calculus and current extension of the resolvent mapping. (English)
[J] Ann. Inst. Fourier 53, No. 3, 903-926 (2003). ISSN 0373-0956; ISSN 1777-5310/e

Consider an $n$-tuple of commuting operators on a Banach space. The present paper discusses several equivalent conditions for the existence of an extension of Taylor's functional calculus to various classes of ultradifferentiable functions. Generalized scalar operators and (variants of) Bishop's property ($\beta$) are also considered.
[Cătălin Badea (Villeneuve d'Ascq)]

MSC 2000:: *47A60 Functional calculus of operators
47A13 Several-variable spectral theory
32A25 Integral representation of holomorphic functions (several variables)

Keywords: functional calculus; commuting operators; generalized scalar operator; Bishop's property beta; Taylor spectrum; current; ultradifferentiable function; resolvent mapping

Cited in: Zbl 1071.47018

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