JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (6): 112-117.doi: 10.6040/j.issn.1671-9352.0.2018.584

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Consistent invertibility and the judgement of Weyls theorem

LIU Ying, CAO Xiao-hong*   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China
  • Published:2019-06-05

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Abstract: H is an infinite dimensional separable complex Hilbert space and B(H) is the algebra of all bounded linear operators on H. An operator T∈B(H) is said to be “consistent in invertibility” provided that for each S∈B(H), TS and ST are both or neither invertible. Based on the property of consistency in invertibility, we give the necessary and sufficient conditions for T and its functional calculus which the Weyls theorem hold.

Key words: Weyls theorem, spectrum, consistent in invertibility

CLC Number: 

  • O177.2
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