收稿日期: 2012-05-17
修回日期: 2012-07-19
网络出版日期: 2013-07-15
基金资助
陕西师范大学研究生培养创新基金(2012CXS039);陕西师范大学中央高校基本科研专项资金(GK200901015)资助
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
史维娟 , 曹小红 . 2×2上三角算子矩阵单值延拓性质稳定性的判定[J]. 中国科学院大学学报, 2013 , 30(4) : 450 -453 . DOI: 10.7523/j.issn.2095-6134.2013.04.004
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).
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