JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (8): 15-21.doi: 10.6040/j.issn.1671-9352.0.2015.530

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Weyls theorem for the cube of operator and compact perturbations

DONG Jiong, CAO Xiao-hong*   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China
  • Received:2015-11-09 Online:2016-08-20 Published:2016-08-08

Abstract: An operator T∈B(H) is said to satisfy Weyls theorem if σ(T)\σw(T)=π00(T). T∈B(H) is said to have the compact perturbations of Weyls theorem if T+K satisfies Weyls theorem for all compact operators K∈B(H). In this note, a variant of the Weyl spectrum is discussed. Using the variant, we characterize the conditions for T 3 and T satisfying the compact perturbations of Weyls theorem.

Key words: Weyls theorem, compact perturbations, Weyl-Kato decomposition

CLC Number: 

  • O177.2
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