一致可逆性质与Weyl定理的判定

doi:10.6040/j.issn.1671-9352.0.2018.584

摘要/Abstract

摘要： 令H表示无限维复可分的Hilbert空间,B(H)为H上有界线性算子的全体。对算子T∈B(H)而言, 若对于任意算子S∈B(H),TS和ST同时可逆或同时不可逆,则称算子T为一致可逆算子。本文根据算子的一致可逆性质,给出了算子T与其算子演算满足Weyl定理的充要条件。

关键词: Weyl定理, 谱, 一致可逆性质

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

中图分类号:

O177.2

刘萤,曹小红. 一致可逆性质与Weyl定理的判定[J]. 《山东大学学报(理学版)》, 2019, 54(6): 112-117.

LIU Ying, CAO Xiao-hong. Consistent invertibility and the judgement of Weyls theorem[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(6): 112-117.

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