On Certain Aspects of the MultidimensionalS-Spectral Theory

Abstract

This paper has two parts. The first one provides the preliminary notions introducing certain general concepts, in order to study, in the second part, the properties of some operator systems which admit spectral residual decompositions,S-decomposable,S-spectral, andAS-scalar systems, and so forth. The results obtained by Frunză, 1975, are generalized, taking the results of Foias, 1963, as a model and adopting them.