On joint spectra of families of Operator Pencils.

Abstract

In this paper, we introduce and study the basic properties of several
types of joint spectra of n-tuples of operator pencils in both Banach algebra
and Banach space. We give spectral properties (i.e. compactness, the spectral
mapping theorem), as well as an example of the upper and lower triangular
matrices. In addition, we describe the joint spectrum of the tensor product of
several operators.