In this article, the generalized reflexive solution of matrix equations （AX = B, XC = D） is considered. With special properties of generalized reflexive matrices, the necessary and sufficient conditions for the solv...In this article, the generalized reflexive solution of matrix equations （AX = B, XC = D） is considered. With special properties of generalized reflexive matrices, the necessary and sufficient conditions for the solvability and the general expression of the solution are obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set is solved.展开更多
We construct a triangular algebra whose diagonals form a noncommutative algebra and its lattice of invariant projections contains only two nontrivial projections. Moreover we prove that our triangular algebra is maximal.
In this paper, we first consider the least-squares solution of the matrix inverse problem as follows： Find a hermitian anti-reflexive matrix corresponding to a given generalized reflection matrix J such that for give...In this paper, we first consider the least-squares solution of the matrix inverse problem as follows： Find a hermitian anti-reflexive matrix corresponding to a given generalized reflection matrix J such that for given matrices X, B we have minA ｜｜AX - B｜｜. The existence theorems are obtained, and a general representation of such a matrix is presented. We denote the set of such matrices by SE. Then the matrix nearness problem for the matrix inverse problem is discussed. That is： Given an arbitrary A^＊, find a matrix A E SE which is nearest to A^＊ in Frobenius norm. We show that the nearest matrix is unique and provide an expression for this nearest matrix.展开更多
By applying the multiple quotient singular value decomposition QQQQQ-SVD, we study the block independence in g-inverse and reflexive inner inverse of 2× 2 partitioned matrices, and prove a conjecture in [Yiju Wan...By applying the multiple quotient singular value decomposition QQQQQ-SVD, we study the block independence in g-inverse and reflexive inner inverse of 2× 2 partitioned matrices, and prove a conjecture in [Yiju Wang, SIAM J. Matrix Anal. Appl., 19（2）, 407-415（1998）].展开更多
Let N be a maximal and discrete nest on a separable Hilbert space H,E the projection from H onto the subspace[C]spanned by a particular separating vector for N′and Q the projection from K=H⊕H onto the closed subspac...Let N be a maximal and discrete nest on a separable Hilbert space H,E the projection from H onto the subspace[C]spanned by a particular separating vector for N′and Q the projection from K=H⊕H onto the closed subspace{(,):∈H}.Let L be the closed lattice in the strong operator topology generated by the projections(E 00 0),{(E 00 0):E∈N}and Q.We show that L is a Kadison-Singer lattice with trivial commutant,i.e.,L′=CI.Furthermore,we similarly construct some Kadison-Singer lattices in the matrix algebras M2n(C)and M2n.1(C).展开更多
We show that many Kadison-Singer algebras are maximal triangular in all algebras containing them although their definition requires the maximality taken in the class of reflexive algebras. Diagonal-trivial maximal non...We show that many Kadison-Singer algebras are maximal triangular in all algebras containing them although their definition requires the maximality taken in the class of reflexive algebras. Diagonal-trivial maximal non self-adjoint subalgebras of matrix algebras with lower dimensions are classified.展开更多
In this paper,the Hermitian reflexive（Anti-Hermitian reflexive）least-squares so-lutions of matrix equations（AX = B,XC = D）are considered.With special properties of partitioned matrices and Hermitian reflexive（Ant...In this paper,the Hermitian reflexive（Anti-Hermitian reflexive）least-squares so-lutions of matrix equations（AX = B,XC = D）are considered.With special properties of partitioned matrices and Hermitian reflexive（Anti-Hermitian reflexive）matrices,the general expression of the solution is obtained.Moreover,the related optimal approximation problem to a given matrix over the solution set is considered.展开更多
We derive necessary and sufficient conditions for the existence and an expression of the （anti）reflexive solution with respect to the nontrivial generalized reflection matrix P to the system of complex matrix equati...We derive necessary and sufficient conditions for the existence and an expression of the （anti）reflexive solution with respect to the nontrivial generalized reflection matrix P to the system of complex matrix equations AX = B and XC = D. The explicit solutions of the approximation problem min x∈Ф ｜｜X - E｜｜F was given, where E is a given complex matrix and Ф is the set of all reflexive （or antireflexive） solutions of the system mentioned above, and ｜｜·｜｜ is the Frobenius norm. Furthermore, it was pointed that some results in a recent paper are special cases of this paper.展开更多
Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed poin...Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map- pings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con- vex optimization problems, and split feasibility problems. Our result extends many recent important results.展开更多
In this paper we present sufficient conditions for reflexivity of any powers of the multiplication operator acting on Banach spaces of formal Laurent series.
基金supported by National Natural Science Foundation of China (10571047)and by Scientific Research Fund of Hunan Provincial Education Department of China Grant(06C235)+1 种基金by Central South University of Forestry and Technology (06Y017)by Specialized Research Fund for the Doctoral Program of Higher Education (20060532014)
文摘In this article, the generalized reflexive solution of matrix equations （AX = B, XC = D） is considered. With special properties of generalized reflexive matrices, the necessary and sufficient conditions for the solvability and the general expression of the solution are obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set is solved.
基金Shaanxi Natural Science Foundation of China (Grant No. 2006A17)
文摘We construct a triangular algebra whose diagonals form a noncommutative algebra and its lattice of invariant projections contains only two nontrivial projections. Moreover we prove that our triangular algebra is maximal.
基金supported by China Postdoctoral Science Foundation (Grant No. 2004035645)
文摘In this paper, we first consider the least-squares solution of the matrix inverse problem as follows： Find a hermitian anti-reflexive matrix corresponding to a given generalized reflection matrix J such that for given matrices X, B we have minA ｜｜AX - B｜｜. The existence theorems are obtained, and a general representation of such a matrix is presented. We denote the set of such matrices by SE. Then the matrix nearness problem for the matrix inverse problem is discussed. That is： Given an arbitrary A^＊, find a matrix A E SE which is nearest to A^＊ in Frobenius norm. We show that the nearest matrix is unique and provide an expression for this nearest matrix.
基金the National Natural Science Foundation of China,Grant No.10371044
文摘By applying the multiple quotient singular value decomposition QQQQQ-SVD, we study the block independence in g-inverse and reflexive inner inverse of 2× 2 partitioned matrices, and prove a conjecture in [Yiju Wang, SIAM J. Matrix Anal. Appl., 19（2）, 407-415（1998）].
基金supported by National Natural Science Foundation of China(Grant No.11271390)Natural Science Foundation Project of ChongQing,Chongqing Science Technology Commission(Grant No.2010BB9318)
文摘Let N be a maximal and discrete nest on a separable Hilbert space H,E the projection from H onto the subspace[C]spanned by a particular separating vector for N′and Q the projection from K=H⊕H onto the closed subspace{(,):∈H}.Let L be the closed lattice in the strong operator topology generated by the projections(E 00 0),{(E 00 0):E∈N}and Q.We show that L is a Kadison-Singer lattice with trivial commutant,i.e.,L′=CI.Furthermore,we similarly construct some Kadison-Singer lattices in the matrix algebras M2n(C)and M2n.1(C).
基金Supported by National Natural Science Foundation of China(Grant No.11371290)
文摘We show that many Kadison-Singer algebras are maximal triangular in all algebras containing them although their definition requires the maximality taken in the class of reflexive algebras. Diagonal-trivial maximal non self-adjoint subalgebras of matrix algebras with lower dimensions are classified.
文摘In this paper,the Hermitian reflexive（Anti-Hermitian reflexive）least-squares so-lutions of matrix equations（AX = B,XC = D）are considered.With special properties of partitioned matrices and Hermitian reflexive（Anti-Hermitian reflexive）matrices,the general expression of the solution is obtained.Moreover,the related optimal approximation problem to a given matrix over the solution set is considered.
基金supported by the National Natural Science Foundation of China （Grant No.60672160）
文摘We derive necessary and sufficient conditions for the existence and an expression of the （anti）reflexive solution with respect to the nontrivial generalized reflection matrix P to the system of complex matrix equations AX = B and XC = D. The explicit solutions of the approximation problem min x∈Ф ｜｜X - E｜｜F was given, where E is a given complex matrix and Ф is the set of all reflexive （or antireflexive） solutions of the system mentioned above, and ｜｜·｜｜ is the Frobenius norm. Furthermore, it was pointed that some results in a recent paper are special cases of this paper.
文摘Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map- pings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con- vex optimization problems, and split feasibility problems. Our result extends many recent important results.
文摘In this paper we present sufficient conditions for reflexivity of any powers of the multiplication operator acting on Banach spaces of formal Laurent series.
