This paper is devoted to studying the representation of measures of non-generalized compactness,in particular,measures of noncompactness,of non-weak compactness and of non-super weak compactness,defined on Banach spac...This paper is devoted to studying the representation of measures of non-generalized compactness,in particular,measures of noncompactness,of non-weak compactness and of non-super weak compactness,defined on Banach spaces and its applications.With the aid of a three-time order-preserving embedding theorem,we show that for every Banach space X,there exist a Banach function space C(K)for some compact Hausdorff space K and an order-preserving affine mapping T from the super space B of all the nonempty bounded subsets of X endowed with the Hausdorff metric to the positive cone C(K)^(+) of C(K),such that for every convex measure,in particular,the regular measure,the homogeneous measure and the sublinear measure of non-generalized compactnessμon X,there is a convex function F on the cone V=T(B)which is Lipschitzian on each bounded set of V such that F(T(B))=μ(B),■B∈B.As its applications,we show a class of basic integral inequalities related to an initial value problem in Banach spaces,and prove a solvability result of the initial value problem,which is an extension of some classical results due to Bana′s and Goebel(1980),Goebel and Rzymowski(1970)and Rzymowski(1971).展开更多
In general, Banach space-valued Riemann integrable functions defined on [0, 1] （equipped with the Lebesgue measure） need not be weakly continuous almost everywhere. A Banach space is said to have the weak Lebesgue p...In general, Banach space-valued Riemann integrable functions defined on [0, 1] （equipped with the Lebesgue measure） need not be weakly continuous almost everywhere. A Banach space is said to have the weak Lebesgue property if every Riemann integrable function taking values in it is weakly continuous almost everywhere. In this paper we discuss this property for the Banach space LX^1 of all Bochner integrable functions from [0, 1] to the Banach space X. We show that LX^1 has the weak Lebesgue property whenever X has the Radon-Nikodym property and X＊ is separable. This generalizes the result by Chonghu Wang and Kang Wan [Rocky Mountain J. Math., 31（2）, 697-703 （2001）] that L^1[0, 1] has the weak Lebesgue property.展开更多
The higher spin operator of several R^(6)variables is an analogue of the■-operator in theory of several complex variables.The higher spin representation of so6(C)is⊙^(k)C_(4)and the higher spin operator D_(k) acts o...The higher spin operator of several R^(6)variables is an analogue of the■-operator in theory of several complex variables.The higher spin representation of so6(C)is⊙^(k)C_(4)and the higher spin operator D_(k) acts on⊙^(k)C_(4)-valued functions.In this paper,the authors establish the Bochner-Martinelli formula for higher spin operator Dk of several R^(6)variables.The embedding of R^(6n) into the space of complex 4n×4 matrices allows them to use two-component notation,which makes the spinor calculus on R^(6n)more concrete and explicit.A function annihilated by D_(k ) is called k-monogenic.They give the Penrose integral formula over R^(6n) and construct many k-monogenic polynomials.展开更多
在量子信息理论中,量子纠缠态是一种非常重要的资源.探测给定量子态的纠缠性是一个极其重要的研究课题.2001年,Nielsen M A提出了一个判断两体量子态纠缠性的约化判据.之后,2005年William Hall又提出了一个有限维多体复合系统量子态的...在量子信息理论中,量子纠缠态是一种非常重要的资源.探测给定量子态的纠缠性是一个极其重要的研究课题.2001年,Nielsen M A提出了一个判断两体量子态纠缠性的约化判据.之后,2005年William Hall又提出了一个有限维多体复合系统量子态的约化判据.将上述两类判据推广到了无限维多体量子系统情形,给出了无限维多体量子态全可分的两类约化判据.展开更多
Several results about convolution and about Fourier coefficients for X-valued functions defined on t he torus satisfying the condition sup ｜｜y｜｜=1∫-π^π｜｜ B （f （e^iθ）, y）｜｜dθ/2π〈 ∞ for a bounded bil...Several results about convolution and about Fourier coefficients for X-valued functions defined on t he torus satisfying the condition sup ｜｜y｜｜=1∫-π^π｜｜ B （f （e^iθ）, y）｜｜dθ/2π〈 ∞ for a bounded bilinear map B ： X × Y → Z are presented and some applications are given.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11731010)。
文摘This paper is devoted to studying the representation of measures of non-generalized compactness,in particular,measures of noncompactness,of non-weak compactness and of non-super weak compactness,defined on Banach spaces and its applications.With the aid of a three-time order-preserving embedding theorem,we show that for every Banach space X,there exist a Banach function space C(K)for some compact Hausdorff space K and an order-preserving affine mapping T from the super space B of all the nonempty bounded subsets of X endowed with the Hausdorff metric to the positive cone C(K)^(+) of C(K),such that for every convex measure,in particular,the regular measure,the homogeneous measure and the sublinear measure of non-generalized compactnessμon X,there is a convex function F on the cone V=T(B)which is Lipschitzian on each bounded set of V such that F(T(B))=μ(B),■B∈B.As its applications,we show a class of basic integral inequalities related to an initial value problem in Banach spaces,and prove a solvability result of the initial value problem,which is an extension of some classical results due to Bana′s and Goebel(1980),Goebel and Rzymowski(1970)and Rzymowski(1971).
基金supported by MEC and FEDER (Project MTM2005-08350-C03-03)Generalitat Valenciana (Project GV/2007/191)+3 种基金supported by MEC and FEDER (Project MTM2005-08379)Fundacion Seneca (Project 00690/PI/04) the "Juan de la Cierva" Programme (MEC and FSE)supported by MEC and FEDER (Project MTM2006-11690-C02-01)
文摘In general, Banach space-valued Riemann integrable functions defined on [0, 1] （equipped with the Lebesgue measure） need not be weakly continuous almost everywhere. A Banach space is said to have the weak Lebesgue property if every Riemann integrable function taking values in it is weakly continuous almost everywhere. In this paper we discuss this property for the Banach space LX^1 of all Bochner integrable functions from [0, 1] to the Banach space X. We show that LX^1 has the weak Lebesgue property whenever X has the Radon-Nikodym property and X＊ is separable. This generalizes the result by Chonghu Wang and Kang Wan [Rocky Mountain J. Math., 31（2）, 697-703 （2001）] that L^1[0, 1] has the weak Lebesgue property.
基金supported by the National Nature Science Foundation of China(Nos.12101564,11801508,11801523)the Nature Science Foundation of Zhejiang Province(No.LY22A010013)。
文摘The higher spin operator of several R^(6)variables is an analogue of the■-operator in theory of several complex variables.The higher spin representation of so6(C)is⊙^(k)C_(4)and the higher spin operator D_(k) acts on⊙^(k)C_(4)-valued functions.In this paper,the authors establish the Bochner-Martinelli formula for higher spin operator Dk of several R^(6)variables.The embedding of R^(6n) into the space of complex 4n×4 matrices allows them to use two-component notation,which makes the spinor calculus on R^(6n)more concrete and explicit.A function annihilated by D_(k ) is called k-monogenic.They give the Penrose integral formula over R^(6n) and construct many k-monogenic polynomials.
文摘在量子信息理论中,量子纠缠态是一种非常重要的资源.探测给定量子态的纠缠性是一个极其重要的研究课题.2001年,Nielsen M A提出了一个判断两体量子态纠缠性的约化判据.之后,2005年William Hall又提出了一个有限维多体复合系统量子态的约化判据.将上述两类判据推广到了无限维多体量子系统情形,给出了无限维多体量子态全可分的两类约化判据.
文摘Several results about convolution and about Fourier coefficients for X-valued functions defined on t he torus satisfying the condition sup ｜｜y｜｜=1∫-π^π｜｜ B （f （e^iθ）, y）｜｜dθ/2π〈 ∞ for a bounded bilinear map B ： X × Y → Z are presented and some applications are given.
文摘本文通过类似Stieltjes积分的处理,对在Banach空间取值的向量值函数f(t)和数值函数 g(t)定义integral from n=a to b(g(t)df(t) 、integral from n=a to b(f(t)dg(t)), 从而将其结果推广到Bochner可积的向量值函数。
