In this paper,a-Browder’s theorem and a-Weyl’s theorem for bounded linear operators are studied by means of the property of the topological uniform descent.The sufficient and necessary conditions for a bounded linea...In this paper,a-Browder’s theorem and a-Weyl’s theorem for bounded linear operators are studied by means of the property of the topological uniform descent.The sufficient and necessary conditions for a bounded linear operator defined on a Hilbert space holding aBrowder’s theorem and a-Weyl’s theorem are established.As a consequence of the main result,the new judgements of a-Browder’s theorem and a-Weyl’s theorem for operator function are discussed.展开更多
Let H be a complex infinite dimensional Hilbert space and B(H)be the algebra of all bounded linear operators on H.In this paper,we mainly study the operators that satisfy both a-Weyl's theorem and property(R).Also...Let H be a complex infinite dimensional Hilbert space and B(H)be the algebra of all bounded linear operators on H.In this paper,we mainly study the operators that satisfy both a-Weyl's theorem and property(R).Also,the operators whose functional calculus satisfies the two properties are also explored.We give the features for the operator or its functional calculus for which both a-Weyl's theorem and property(R)hold.展开更多
基金Supported by the 2021 General Special Scientific Research Project of Education Department of Shaanxi Provincial Government(21JK0637)Science and Technology Planning Project of Weinan Science and Technology Bureau(2022ZDYFJH-11)2021 Talent Project of Weinan Normal University(2021RC16)。
文摘In this paper,a-Browder’s theorem and a-Weyl’s theorem for bounded linear operators are studied by means of the property of the topological uniform descent.The sufficient and necessary conditions for a bounded linear operator defined on a Hilbert space holding aBrowder’s theorem and a-Weyl’s theorem are established.As a consequence of the main result,the new judgements of a-Browder’s theorem and a-Weyl’s theorem for operator function are discussed.
基金Supported by the National Natural Science Foundation of China(Grant No.11671201)。
文摘Let H be a complex infinite dimensional Hilbert space and B(H)be the algebra of all bounded linear operators on H.In this paper,we mainly study the operators that satisfy both a-Weyl's theorem and property(R).Also,the operators whose functional calculus satisfies the two properties are also explored.We give the features for the operator or its functional calculus for which both a-Weyl's theorem and property(R)hold.
