On the localization of the spectrum for systems of operators

Abstract:

Let $a = ({a_1}, \ldots ,{a_n})$ be a commuting system of linear continuous operators on a complex Banach space X. We show that, for any $x \in X$, the local analytic spectrum $\sigma (a,x)$ [1] is contained in the spectral hull of the local spectrum ${\text {sp}}(a,x)$ [4].