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›› 2013, Vol. 30 ›› Issue (2): 159-165.DOI: 10.7523/j.issn.1002-1175.2013.02.003

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Generalized Kato decomposition and perturbations of the single-valued extension property

XIAO Na-Na, CAO Xiao-Hong   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, China
  • Received:2012-03-05 Revised:2012-04-26 Online:2013-03-15

Abstract:

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.

Key words: single-valued extension property, compact perturbation, generalized Kato decomposition

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