收稿日期: 2012-03-05
修回日期: 2012-04-26
网络出版日期: 2012-04-26
基金资助
陕西师范大学中央高校基本科研业务费专项资金(GK200901015)资助
Generalized Kato decomposition and perturbations of the single-valued extension property
Received date: 2012-03-05
Revised date: 2012-04-26
Online published: 2012-04-26
肖娜娜 , 曹小红 . 广义Kato分解及单值延拓性质的摄动[J]. 中国科学院大学学报, 2013 , 30(2) : 159 -165 . DOI: 10.7523/j.issn.1002-1175.2013.02.003
A Hilbert space operator T has the single-valued extension property if the only analytic function f which satisfies (T-λI)f(λ)=0 is f≡0. Obviously the point spectrum of any operator which has empty interior must have the single-valued extension property. Using the spectrum derived from "generalized Kato decomposition", we investigate stability of the single-valued extension property under compact perturbations. Also, we characterize the 2×2 upper triangular operator matrix for which the single-valued extension property is stable under compact perturbations.
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