Pseudospectra in a non-Archimedean Banach space and essential pseudospectra in Eω

Abstract

In this work, we introduce and study the pseudospectra and the essential pseudospectra of linear operators in a non-Archimedean Banach space and in the non-Archimedean Hilbert space E ω , respectively. In particular, we characterize these pseudospectra. Furthermore, inspired by T. Diagana and F. Ramaroson [12], we establish a relationship between the essential pseudospectrum of a closed linear operator and the essential pseudospectrum of this closed linear operator perturbed by completely continuous operator in the non-Archimedean Hilbert space E ω .

A note on pencil of bounded linear operators on non-archimedean Banach spaces

“…When X = Y, if A \in \scrL (X) and B is unbounded linear operator, then A + B is closed if and only if B is closed [3]. For more details on non-archimedean operators theory, we refer to [2,3,7]. There are many interesting works on pseudospectra in the classical Banach space, see [4,9].…”