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Journal of University of Chinese Academy of Sciences ›› 2013, Vol. 30 ›› Issue (4): 450-453.DOI: 10.7523/j.issn.2095-6134.2013.04.004

• Research Articles • Previous Articles     Next Articles

Stability of single-valued extension property for 2×2 upper triangular operators

SHI Wei-Juan, CAO Xiao-Hong   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, China
  • Received:2012-05-17 Revised:2012-07-19 Online:2013-07-15

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, CB(H), MC=450, then there exists δ>0 such that MC+K∈(SVEP) for all CB(H) and for all Kκ(HH) with ‖K‖<δ if and only if 1) there exists δ>0 such that A+K∈(SVEP), B+K∈(SVEP) for all Kκ(H) with ‖K‖<δ, and 2) ρSF(A)∩ρSF(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 ρSF(A) denotes the semi-Fredholm domain of TB(H).

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

CLC Number: