On joint spectra of families of unbounded operators

A. R. Mirotin

Izvestiya. Mathematics , Tome 79 (2015) no. 6, pp. 1235-1259.

Résumé

We consider several types of joint spectra of a finite set of commuting closed operators in a Banach space. We establish new relations between these spectra (it was previously known only that the Taylor spectrum is contained in the commutant spectrum) and prove spectral mapping theorems in the case of generators of semigroups. Some of these theorems generalize previous results of the author. The results obtained are applied to stability issues for multi-parameter semigroups.

Détail

Keywords: unbounded operator, joint spectrum, Bernstein function, Bochner–Philips functional calculus, spectral mapping theorem, multi-parameter operator semigroup, uniform stability, strong stability, abstract Cauchy problem.

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