Journal of University of Chinese Academy of Sciences >
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
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.
XIAO Na-Na , CAO Xiao-Hong . Generalized Kato decomposition and perturbations of the single-valued extension property[J]. Journal of University of Chinese Academy of Sciences, 2013 , 30(2) : 159 -165 . DOI: 10.7523/j.issn.1002-1175.2013.02.003
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