A method to construct strongly non regular order bounded operators from a classical Banach lattice C into any separable Banach lattice F without Dedekind σ completeness is presented in this paper. A r...A method to construct strongly non regular order bounded operators from a classical Banach lattice C into any separable Banach lattice F without Dedekind σ completeness is presented in this paper. A result concerning the order bounded norm and the regular norm is also contained.展开更多
There have been many really positive results co ncerning the weakly compact operators on Banach lattices in terms of their order structure as well as in many respects. This paper will survey some known recent result...There have been many really positive results co ncerning the weakly compact operators on Banach lattices in terms of their order structure as well as in many respects. This paper will survey some known recent results in this area.展开更多
The Carleson measures for weighted Dirichlet spaces had been characterized by Girela and Peláez,who also characterized the boundedness of Volterra type operators between weighted Dirichlet spaces.However,their ch...The Carleson measures for weighted Dirichlet spaces had been characterized by Girela and Peláez,who also characterized the boundedness of Volterra type operators between weighted Dirichlet spaces.However,their characterizations for the boundedness are not complete.In this paper,the author completely characterizes the boundedness and compactness of Volterra type operators from the weighted Dirichlet spaces D^(p)_(α)to _(Dβ)^(q)(-1<α,βand 0<p<q<∞),which essentially complete their works.Furthermore,the author investigates the order boundedness of Volterra type operators between weighted Dirichlet spaces.展开更多
In this paper we define measures of semi noncompactness in a locally convex topological linear space with respect to a given seminorm. Then we get a fixed point theorem for a class of condensing set valued mappings...In this paper we define measures of semi noncompactness in a locally convex topological linear space with respect to a given seminorm. Then we get a fixed point theorem for a class of condensing set valued mappings and apply it to differential inclusions.展开更多
In this paper, the notion of the bounded compact approximation property （BCAP） of a pair [Banach space and its subspace] is used to prove that if X is a closed subspace of Eoo with the BCAP, then L∞/X has the BCAP....In this paper, the notion of the bounded compact approximation property （BCAP） of a pair [Banach space and its subspace] is used to prove that if X is a closed subspace of Eoo with the BCAP, then L∞/X has the BCAP. We also show that X＊ has the A-BCAP with conjugate operators if and only if the pair （X, Y） has the A-BCAP for each finite codimensional subspace Y C X. Let M be a closed subspace of X such that M~ is complemented in X＊. If X has the （bounded） approximation property of order p, then M has the （bounded） approximation property of order p.展开更多
In this paper the existence of discrete vector solutions with bounded second order quotientsfor the difference systems of nonlinear parabolic system is established by the fixed point technique,and then the absolute an...In this paper the existence of discrete vector solutions with bounded second order quotientsfor the difference systems of nonlinear parabolic system is established by the fixed point technique,and then the absolute and relative stability for the general difference schemes is justified in thesense of continuous dependence of the discrete vector solution of the difference schemes on thediscrete data of the original problems.展开更多
文摘A method to construct strongly non regular order bounded operators from a classical Banach lattice C into any separable Banach lattice F without Dedekind σ completeness is presented in this paper. A result concerning the order bounded norm and the regular norm is also contained.
文摘There have been many really positive results co ncerning the weakly compact operators on Banach lattices in terms of their order structure as well as in many respects. This paper will survey some known recent results in this area.
基金supported by the National Natural Science Foundation of China(No.11801094)。
文摘The Carleson measures for weighted Dirichlet spaces had been characterized by Girela and Peláez,who also characterized the boundedness of Volterra type operators between weighted Dirichlet spaces.However,their characterizations for the boundedness are not complete.In this paper,the author completely characterizes the boundedness and compactness of Volterra type operators from the weighted Dirichlet spaces D^(p)_(α)to _(Dβ)^(q)(-1<α,βand 0<p<q<∞),which essentially complete their works.Furthermore,the author investigates the order boundedness of Volterra type operators between weighted Dirichlet spaces.
文摘In this paper we define measures of semi noncompactness in a locally convex topological linear space with respect to a given seminorm. Then we get a fixed point theorem for a class of condensing set valued mappings and apply it to differential inclusions.
基金supported by National Natural Science Foundation of China(Grant Nos.10526034 and 10701063)the Fundamental Research Funds for the Central Universities(Grant No.2011121039)supported by NSF(Grant Nos.DMS-0800061 and DMS-1068838)
文摘In this paper, the notion of the bounded compact approximation property （BCAP） of a pair [Banach space and its subspace] is used to prove that if X is a closed subspace of Eoo with the BCAP, then L∞/X has the BCAP. We also show that X＊ has the A-BCAP with conjugate operators if and only if the pair （X, Y） has the A-BCAP for each finite codimensional subspace Y C X. Let M be a closed subspace of X such that M~ is complemented in X＊. If X has the （bounded） approximation property of order p, then M has the （bounded） approximation property of order p.
文摘In this paper the existence of discrete vector solutions with bounded second order quotientsfor the difference systems of nonlinear parabolic system is established by the fixed point technique,and then the absolute and relative stability for the general difference schemes is justified in thesense of continuous dependence of the discrete vector solution of the difference schemes on thediscrete data of the original problems.
