In this paper, continuous homogeneous selections for the set-valued metric generalized inverses T^ of linear operators T in Banach spaces are investigated by means of the methods of geometry of Banach spaces. Necessar...In this paper, continuous homogeneous selections for the set-valued metric generalized inverses T^ of linear operators T in Banach spaces are investigated by means of the methods of geometry of Banach spaces. Necessary and sufficient conditions for bounded linear operators T to have continuous homogeneous selections for the set-valued metric generalized inverses T~ are given. The results are an answer to the problem posed by Nashed and Votruba.展开更多
In this paper, we introduce the concepts of generalized regular points and narrow spectrum points of bounded linear operators on Hilbert spaces. The concept of generalized regular points is an extension of the concept...In this paper, we introduce the concepts of generalized regular points and narrow spectrum points of bounded linear operators on Hilbert spaces. The concept of generalized regular points is an extension of the concept regular points, and so, the set of all spectrum points is reduced to the narrow spectrum. We present not only the same and different properties of spectrum and of narrow spectrum but also show the relationship between them. Finally, the well known problem about the invariant subspaces of bounded linear operators on separable Hilbert spaces is simplified to the problem of the operator with narrow spectrum only.展开更多
基金supported by National Science Foundation of China (Grant No.11071051)Youth Science Foundation of Heilongjiang Province of China (Grant No.QC2009C73)+1 种基金the second author is supported by the State Committee for Scientific Research of Poland (Grant No.N N201 362236)the third author is supported by National Science Foundation of China (Grant No.11071051)
文摘In this paper, continuous homogeneous selections for the set-valued metric generalized inverses T^ of linear operators T in Banach spaces are investigated by means of the methods of geometry of Banach spaces. Necessary and sufficient conditions for bounded linear operators T to have continuous homogeneous selections for the set-valued metric generalized inverses T~ are given. The results are an answer to the problem posed by Nashed and Votruba.
基金Supported by National Natural Science Foundation of China (Grant No. 11071051)Youth Science Foundation of Heilongjiang Province (Grant No. QC2009C73)the State Committee for Scientific Research of Poland (Grant No. N N201 362236)
文摘In this paper, we introduce the concepts of generalized regular points and narrow spectrum points of bounded linear operators on Hilbert spaces. The concept of generalized regular points is an extension of the concept regular points, and so, the set of all spectrum points is reduced to the narrow spectrum. We present not only the same and different properties of spectrum and of narrow spectrum but also show the relationship between them. Finally, the well known problem about the invariant subspaces of bounded linear operators on separable Hilbert spaces is simplified to the problem of the operator with narrow spectrum only.
