Some spectral sets of linear operators pencils on non-archimedean Banach spaces

Abstract

In this paper, we define the notions of trace pseudo-spectrum, ε−determinant spectrum, and ε−trace of bounded linear operator pencils on non-Archimedean Banach spaces. Many results are proved about trace pseudo-spectrum, ε−determinant spectrum, and ε−trace of bounded linear operator pencils on non-Archimedean Banach spaces. Examples are given to support our work.

Pseudo-spectrum of non-Archimedean matrix pencils

“…Let A ∈ M n (K), the trace and the determinant of A are denoted by T r(A) and det(A) respectively. For more details, we refer to [1], [2], [3], [7] and [9]. We have the following definitions.…”