In this paper, we present some necessary and sufficient conditions for the ex- istence of solutions, hermitian solutions and positive solutions to the system of operator equations AXB = C = BXA in the setting of bound...In this paper, we present some necessary and sufficient conditions for the ex- istence of solutions, hermitian solutions and positive solutions to the system of operator equations AXB = C = BXA in the setting of bounded linear operators on a Hilbert space. Moreover, we obtain the general forms of solutions, hermitian solutions and positive solutions to the system above.展开更多
Let X be an infinite-dimensional real or complex Banach space,and B(X)the Banach algebra of all bounded linear operators on X.In this paper,given any non-negative integer n,we characterize the surjective additive maps...Let X be an infinite-dimensional real or complex Banach space,and B(X)the Banach algebra of all bounded linear operators on X.In this paper,given any non-negative integer n,we characterize the surjective additive maps on B(X)preserving Fredholm operators with fixed nullity or defect equal to n in both directions,and describe completely the structure of these maps.展开更多
Let H be a Hilbert space and A ■ B(H) be a C~*-subalgebra. This paper is devoted to studying the set gP of generalized projections in A from a differential geometric point of view, and mainly focuses on geodesic curv...Let H be a Hilbert space and A ■ B(H) be a C~*-subalgebra. This paper is devoted to studying the set gP of generalized projections in A from a differential geometric point of view, and mainly focuses on geodesic curves. We prove that the space gP is a C~∞ Banach submanifold of A, and a homogeneous reductive space under the action of Banach Lie group U_A of A. Moreover, we compute the geodesics of gP in a standard fashion, and prove that any generalized projection in a prescribed neighbourhood of p∈gP can be joined with p by a unique geodesic curve in gP.展开更多
基金supported by the National Natural Science Foundation of China(11371233)
文摘In this paper, we present some necessary and sufficient conditions for the ex- istence of solutions, hermitian solutions and positive solutions to the system of operator equations AXB = C = BXA in the setting of bounded linear operators on a Hilbert space. Moreover, we obtain the general forms of solutions, hermitian solutions and positive solutions to the system above.
基金supported by National Natural Science Foundation of China(11771261,11701351)Natural Science Basic Research Plan in Shaanxi Province of China(2018JQ1082)the Fundamental Research Funds for the Central Universities(GK202103007,GK202107014).
文摘Let X be an infinite-dimensional real or complex Banach space,and B(X)the Banach algebra of all bounded linear operators on X.In this paper,given any non-negative integer n,we characterize the surjective additive maps on B(X)preserving Fredholm operators with fixed nullity or defect equal to n in both directions,and describe completely the structure of these maps.
基金supported by National Natural Science Foundation of China(Grant No.11371233)
文摘Let H be a Hilbert space and A ■ B(H) be a C~*-subalgebra. This paper is devoted to studying the set gP of generalized projections in A from a differential geometric point of view, and mainly focuses on geodesic curves. We prove that the space gP is a C~∞ Banach submanifold of A, and a homogeneous reductive space under the action of Banach Lie group U_A of A. Moreover, we compute the geodesics of gP in a standard fashion, and prove that any generalized projection in a prescribed neighbourhood of p∈gP can be joined with p by a unique geodesic curve in gP.
