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Acta Mathematica Sinica, English Series

, Volume 26, Issue 11, pp 2109–2116 | Cite as

On operators satisfying T*|T 2|TT*|T*|2 T

  • Jun Li ShenEmail author
  • Fei Zuo
  • Chang Sen Yang
Article

Abstract

Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce a new class denoted by l-*-A, of operators satisfying T*|T 2|TT*|T*|2 T, and we prove the basic properties of these operators. Using these results, we also prove that if T or T* ∈ l-*-A, then w(f(T)) = f(w(T)), σ ea(f(T)) = f(σ ea(T)) for every fH(σ(T)), where H(σ(T)) denotes the set of all analytic functions on an open neighborhood of σ(T).

Keywords

l-*-A point spectrum joint point spectrum α-Browder’s theorem 

MR(2000) Subject Classification

47B20 47A63 

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of MathematicsXinxiang UniversityXinxiangP. R. China
  2. 2.College of Mathematics and Information ScienceHe’nan Normal UniversityXinxiangP. R. China

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