Continuity of spectrum and approximate point spectrum on operator matrices

AbstractLet X and Y be given Banach spaces. For A∈B(X), B∈B(Y) and C∈B(Y,X), let MC be the operator defined on X⊕Y by MC=[AC0B]. In this paper we give conditions for continuity of τ at MC through continuity of τ at A and B, where τ can be equal to the spectrum or approximate point spectrum

Moving Weyl’s theorem from ⨍(T) to T

Schmoeger has shown that if Weyl's theorem holds for an isoloid Banach space operator T ∈ B(X) with stable index, then it holds for ⨍(T) whenever ⨍ ∈ Holo σ (T) is a function holomorphic on some neighbourhood of the spectrum of T. In this note we establish a converse.peerReviewe

p-Adic Mathematical Physics

A brief review of some selected topics in p-adic mathematical physics is presented.Comment: 36 page