Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (4): 713-719.

Previous Articles     Next Articles

Property (h) and Perturbations

Wurichaihu1,2(), Alatancang3,*()   

  1. 1 School of Mathematical Sciences, Inner Mongolia Normal University, Hohhot 010022
    2 School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021
    3 Hohhot University for Nationalities, Hohhot 010051
  • Received:2018-02-09 Online:2019-08-26 Published:2019-09-11
  • Contact: Alatancang E-mail:wurichaihu19@163.com;alatanca@imu.edu.cn
  • Supported by:
    the NSFC(11561053);the NSFC(11761029);the Natural Science Foundation of Inner Mongolia(2018BS01001);the Research Program of Sciences at Universities of Inner Mongolia Autonomous Region(NJZZ18018);the Research Program of Sciences at Universities of Inner Mongolia Autonomous Region(NJZY18021)

Abstract:

In this paper, we introduce and study the property (h), which extends a-Weyl's theorem. We consider its stability under commuting finite rank and nilpotent perturbations. We prove that property (h) on Banach spaces is related to an important property which has a leading role in local spectral theory:the single-valued extension property. From this result we deduce that property (h) holds for several classes of operators.

Key words: Single-valued extension property, a-Weyl's theorem, Property (h)

CLC Number: 

  • O177.1
Trendmd