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 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 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.
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)
