关键词: 单值延拓性质, 紧摄动, 谱

Abstract:

We characterize 2×2 upper triangular operator matrices for which the single-valued extension property is stable under compact perturbations. We get that: if A, B, C∈B(H), M_C=450, then there exists δ>0 such that M_C+K∈(SVEP) for all C∈B(H) and for all K∈κ(H⊕H) with ‖K‖<δ if and only if 1) there exists δ>0 such that A+K∈(SVEP), B+K∈(SVEP) for all K∈κ(H) with ‖K‖<δ, and 2) ρ_SF(A)∩ρ_SF(B) consists of finite connected components, where B(H) denotes the set of bounded linear operators on H, κ(H) denotes the set of compact operators on H, and ρ_SF(A) denotes the semi-Fredholm domain of T∈B(H).

Key words: single-valued extension property, compact perturbations, spectrum