Condition pseudospectrum of operator pencils on non-archimedean Banach spaces

TL;DR

This paper investigates the condition pseudospectrum and essential condition pseudospectrum of operator pencils on non-archimedean Banach spaces, providing characterizations and relations to the usual spectrum in non-archimedean fields.

Contribution

It offers new characterizations of the condition pseudospectrum and essential spectrum of operator pencils in non-archimedean Banach spaces, linking them to the spectrum in non-archimedean fields.

Findings

Characterization of the condition pseudospectrum of operator pencils.

Relation between the condition pseudospectrum and the usual spectrum.

Characterization of the essential spectrum using non-archimedean completely continuous operators.

Abstract

This paper deals with the condition pseudospectrum and essential condition pseudospectrum of operator pencils on n.a Banach spaces. We give a characterization of the condition pseudospectrum of operator pencils on n.a Banach spaces, the relation between the condition pseudospectrum of $(A,B)$ and the usual spectrum in a n.a valued field is investigated. Finally, we give a characterization of the essential spectrum of $(A,B)$ where $A\neq B$ by means of n.a completely continuous operators and we give some examples.