Abstract
Generalizing a result of [1] and [2], we show that every
-scalar system (see Def. 3) is decomposable (in the sense of [6], [7]). By means of this fact and by some results on decomposable n-tuples (contained in [6] and [7]) we prove the theorem of support and (in the case of an inverse closed admissible algebra
) the spectral mapping theorem for
-functional calculi in several variables (see Def. 3). In the case of a single operator we obtain a simplification of the definition of an
-spectral function (in the sense of [5], Def. 3.1.3).
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Albrecht, E., Frunză, Ş. Non-analytic functional calculi in several variables. Manuscripta Math 18, 327–336 (1976). https://doi.org/10.1007/BF01270493
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DOI: https://doi.org/10.1007/BF01270493