Der spektrale Abbildungssatz für nichtanalytische Funktionalkalküle in mehreren Veränderlichen

In this note we continue the study of -functional calculi in several variables (introduced in 1] and 2]). In the situation of an inverse closed (see Def. 1.2) basic algebra of type I or II we characterize the algebra generated by an arbitrary -functional calculus φ and prove several variants of the spectral mapping theorem, thus generalizing corresponding results of F.-H. Vasilescu 10] (see also the more general version in 4], Th. 3.2.1) to the case of several commuting operators. By means of the spectral mapping theorem we prove the decomposability (in the sense of St. Frunz? 6]) of m-tuples of the type (φ(f₁),..., φ(f_m)) with f₁,...,f_mε .