Structured pseudospectrum and structured essential pseudospectrum of closed linear operator pencils on ultrametric Banach spaces

Abstract

We introduce and study the structured pseudospectrum and the essential pseudospectrum of closed linear operator pencils on ultrametric Banach spaces. We establish a characterization of the structured pseudospectrum of closed linear operator pencils and relationship between the structured pseudospectrum and the structured pseudospectrum of closed linear operator pencils on ultrametric Banach spaces. Many characterizations of structured essential pseudospectra of operators, such as the structured essential pseudospectrum of closed linear operator pencils, is invariant under per- turbation of completely continuous linear operators on ultrametric Banach spaces over Qp. Finally, we give some illustrative examples.