We give the necessary and sufficient condition for a bounded linear operator with property （ω） by means of the induced spectrum of topological uniform descent, and investigate the permanence of property （ω） unde...We give the necessary and sufficient condition for a bounded linear operator with property （ω） by means of the induced spectrum of topological uniform descent, and investigate the permanence of property （ω） under some commuting perturbations by power finite rank operators. In addition, the theory is exemplified in the case of algebraically paranormal operators.展开更多
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
In this note,property （ω）and property 1 （ω）are variants of Weyl’s theorem. By means of topological uniform descent, the sufficient and necessary conditions of a bounded linear operator defined on a Hilbert spac...In this note,property （ω）and property 1 （ω）are variants of Weyl’s theorem. By means of topological uniform descent, the sufficient and necessary conditions of a bounded linear operator defined on a Hilbert space that satisfies property 1 （ω） and property （ω）is studied. Moreover, property 1 （ω）and property （ω）of 2 2operator matrices are discussed as well.展开更多
基金Acknowledgements The authors would like to thank the referees for their many valuable suggestions which have greatly contributed to improve the final form of this paper. This work was supported by the National Natural Science Foundation of China （Grant Nos. 10971011, 11371222）.
文摘We give the necessary and sufficient condition for a bounded linear operator with property （ω） by means of the induced spectrum of topological uniform descent, and investigate the permanence of property （ω） under some commuting perturbations by power finite rank operators. In addition, the theory is exemplified in the case of algebraically paranormal operators.
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 Fundamental Research Funds for the Central Universities(No.GK200901015)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20110202110002)
基金Supported by the Fundamental Research Funds for the Central Universities(GK200901015)Project for Outstanding Young and Middle-aged Researchers initiated by Tianshui Normal University(TSY201205)
文摘In this note,property （ω）and property 1 （ω）are variants of Weyl’s theorem. By means of topological uniform descent, the sufficient and necessary conditions of a bounded linear operator defined on a Hilbert space that satisfies property 1 （ω） and property （ω）is studied. Moreover, property 1 （ω）and property （ω）of 2 2operator matrices are discussed as well.
