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Stability of single-valued extension property for 2×2 upper triangular operators
Received date: 2012-05-17
Revised date: 2012-07-19
Online published: 2013-07-15
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), MC=450, then there exists δ>0 such that MC+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) 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 T∈B(H).
SHI Wei-Juan , CAO Xiao-Hong . Stability of single-valued extension property for 2×2 upper triangular operators[J]. Journal of University of Chinese Academy of Sciences, 2013 , 30(4) : 450 -453 . DOI: 10.7523/j.issn.2095-6134.2013.04.004
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