# On joint spectra of families of unbounded operators

## TL;DR

This paper explores various joint spectra of commuting unbounded operators in Banach spaces, establishes new spectral relations, and proves spectral mapping theorems for semigroup generators, with applications to stability analysis.

## Contribution

It introduces new relations between different joint spectra and generalizes spectral mapping theorems for semigroup generators in Banach spaces.

## Key findings

- New relations between joint spectra established
- Spectral mapping theorems proved for semigroup generators
- Applications to stability of multiparametric semigroups

## 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.