共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we first introduce a lattice decomposition and finite-dimensional lattice decomposition (FDLD) for Banach lattices. Then we show that for a Banach lattice with FDLD, the following are equivalent: (i) it has the Radon-Nikodym property; (ii) it is a KB-space; (iii) it is a Levi space; and (iv) it is a σ-Levi space. We then give a sequential representation of the Fremlin projective tensor product of an atomic Banach lattice with a Banach lattice. Using this sequential representation, we show that if one of the Banach lattices X and Y is atomic, then the Fremlin projective tensor product has the Radon-Nikodym property (or, respectively, is a KB-space) if and only if both X and Y have the Radon-Nikodym property (or, respectively, are KB-spaces). 相似文献
2.
An example of two distinguished Fréchet spaces E, F is given (even more, E is quasinormable and F is normable) such that their completed injective tensor product E?F is not distinguished. On the other hand, it is proved that for arbitrary reflexive Fréchet space E and arbitrary compact set K the space of E - valued continuous functions C(K, E) is distinguished and its strong dual is naturally isomorphic to ? where L1(μ) = C(K)1. 相似文献
3.
Our results describe how quantitative properties of univariate operators are inherited by the tensor product of their parametric extensions. This includes statements concerning simultaneous approximation. The estimates are in terms of partial and total moduli of smoothness of higher order. Applications are given for cubic interpolatory splines and Bernstein operators. Further applications are possible. 相似文献
4.
Banach空间的某类分解 总被引:1,自引:1,他引:0
石峰 《数学物理学报(A辑)》1998,18(3):318-323
该文从Schauder分解出发,考虑了由一类具有特殊基的Banach空间Y所生成的Banach空间Y(Xi,i∈N)(特别是当每个Xi均为Y的标量域)的一些性质,以及它们之间的联系. 相似文献
5.
设F是一个域,a∈F~nF~m.若存在h∈F~m,k∈F~m,使得a=hk,则称a是可分的.空间F~nF~m上的线性算子A称为是强可分的,是指x∈F~nF~m,x可分Ax可分.本文证明了F~nF~n上的线性算子A是强可分的当且仅当存在F~n上的线性双射A_1与A_2,使得A=A_1A_2或A=A_1~T A_2;证明了F~nF~m(n≠m)上线性算子A是强可分的当且仅当存在F~n与F~m上的线性双射A_1与A_2,使得A=A_1A_2.最后,给出了可分算子、强可分算子和秩1保持映射之间的关系. 相似文献
6.
Banach空间上凸泛函的某些对偶性质 总被引:2,自引:0,他引:2
本语文对Banach空间上的凸泛函建立了若干对偶性质,通过对偶的手段,建立了非常简洁的凸泛函极小化序列弱收敛的特征定理。 相似文献
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9.
On Hereditarily Indecomposable Banach Spaces 总被引:1,自引:0,他引:1
Li Xin CHENG Huai Jie ZHONG 《数学学报(英文版)》2006,22(3):751-756
This paper shows that every non-separable hereditarily indecomposable Banach space admits an equivalent strictly convex norm, but its bi-dual can never have such a one; consequently, every non-separable hereditarily indecomposable Banach space has no equivalent locally uniformly convex norm. 相似文献
10.
讨论Banach空间几种超投影性质(及其相应的局部化性质)之间的关系,证明了在Banach空间X自反的条件下,X是lp-次投影空间的充要条件是X*是lp-超投影空间,X是局部lp-次投影空间的充要条件是X*是局部lp-超投影空间,以及X是局部次投影空间的充要条件是X*是局部超投影的。其中1/p+1/q=1(p>1,q>1)。 相似文献
11.
该文主要给出von Neumann-Jordan型常数的一些性质. 首先得到利用von Neumann-Jordan型常数来刻划一致非
方的等价条件. 其次介绍了von Neumann-Jordan型常数与正规结构的关系. 最后介绍了C1'(X)与其他空间常数之间的关系, 例如C1'(X)与C1(X)之间的关系等等. 相似文献
12.
B-空间上凸函数的若干指数性质 总被引:1,自引:0,他引:1
本文引入且用次梯度集该划Banach空间上凸函数的上、下指数,得到共轭凸函数上、下指数间的完整共轭关系、正齐次凸函数是Minkovski规函数的幂等结果,已有的一维相关结果是本文的特例。 相似文献
13.
Sönke Blunck 《Journal of Functional Analysis》2002,195(2):350-370
We extend the Trotter-Kato-Chernoff theory of strong approximation of C0 semigroups on Banach spaces to operator-norm approximation of analytic semigroups with error estimate. As application we obtain a criterion for the operator-norm convergence of the Trotter product formula on Banach spaces with error estimate n−1 log n, provided one of the generators has a bounded H∞ functional calculus. For both results, we present versions for approximation in operator-ideal-norms such as the trace norm or the Hilbert-Schmidt norm. Finally, we give some remarks on the operator-norm convergence of the Trotter product formula for semigroups acting on a scale of Lp-spaces. 相似文献
14.
Elisabetta M. Mangino 《Mathematische Nachrichten》1997,185(1):149-162
15.
Juraj Činčura 《Applied Categorical Structures》1997,5(2):111-122
In this paper symmetric monoidal closed structures on coreflective subcategories of the category of (Hausdorff) topological spaces are studied. We describe all such structures on the category of (Hausdorff) pseudoradial spaces and some of its subcategories and give an example of a coreflective subcategory of the category of Hausdorff topological spaces admitting a proper class of symmetric monoidal closed structures. 相似文献
16.
从y-数值半径的定义出发,利用矩阵张量积与诱导矩阵的性质,研究了它们的y-数值半径,得到了矩阵张量积与诱导矩阵y-数值半径的几个不等式. 相似文献
17.
Saeid Azam 《代数通讯》2013,41(3):905-927
It is known that under certain finite dimensionality condition the derivation algebra of tensor product of two algebras can be obtained in terms of the derivation algebras and the centroids of the involved algebras. We extend this theorem to infinite dimensional case and as an application, we determine the derivation algebra of the fixed point algebra of the tensor product of two algebras, with respect to the tensor product of two finite order automorphisms. These provide the framework for calculating the derivations of some infinite dimensional Lie algebras. 相似文献
18.
Kamil John 《Czechoslovak Mathematical Journal》2005,55(3):677-681
We observe that a separable Banach space X is reflexive iff each of its quotients with Schauder basis is reflexive. Similarly if ℒ(X, Y) is not reflexive for reflexive X and Y then ℒ(X
1, Y) is is not reflexive for some X
1 ⊂ X, X
1 having a basis.
This work was supported by the grants No. 201/03/0041 and No. 201/04/0090 of the Grant Agency of the Czech Republic and by
the grant No. A1019801 of the Academy of Sciences of the Czech Republic. 相似文献
19.
Yongjin Li & Qingying Bu 《数学研究》2016,49(4):429-432
For a Banach space $E$, we give sufficient conditions for the Grothendieck
property of $⨶_{n,s,\pi}E$, the symmetric projective tensor product of $E.$ Moreover, if $E^∗$ has
the bounded compact approximation property, then these sufficient conditions are also
necessary. 相似文献