Funktionalkalk�le f�r abgeschlossene lineare Operatoren in Banachr�umen

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.