On joint spectra of families of unbounded operators

Abstract

In this paper several joint spectra for a finite commuting family of closed operators in Banach space are considered, some new relations between these spectra established (earlier only the inclusion of the Taylor spectrum in the commutant one was known), and in the case of semigroup generators spectral mapping theorems for such spectra are proved. Several of this theorems are generalizations of preceding results due to the author. Applications to stability of multiparametric semigroups are given.