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Funktionalkalküle für abgeschlossene lineare Operatoren in Banachräumen

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Abstract

The theory of A-scalar and generalized scalar operators of Colojoara and Foias [7] is generalized to unbounded closed operators. A spectral mapping theorem is proved for the (local) spectrum. Generalized scalar operators admit a calculus for

, the C⋡-functions on the C⋡-manifold

. B⋡(C), the C⋡-functions onC, which are bounded with all derivatives, is an other admissible algebra. If σ(T) is contained in a generalized circle

, characterisations as in [7] and explicit expressions for the Cm(K)- and the Bm(R)-calculus are obtained.

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  1. Mathematisches Institut, Universität Münster, Roxeler Str. 64, D-4400, Münster

    Erich Marschall

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  1. Erich Marschall
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Marschall, E. Funktionalkalküle für abgeschlossene lineare Operatoren in Banachräumen. Manuscripta Math 35, 277–310 (1981). https://doi.org/10.1007/BF01263264

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  • DOI: https://doi.org/10.1007/BF01263264

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