共查询到20条相似文献,搜索用时 0 毫秒
1.
Jianwen Peng Heung Wing Joseph Lee Xinmin Yang 《Journal of Mathematical Analysis and Applications》2005,302(2):441-449
In this paper, the notion of affinelike set-valued maps is introduced and some properties of these maps are presented. Then a new Hahn-Banach extension theorem with a K-convex set-valued map dominated by an affinelike set-valued map is obtained. 相似文献
2.
Let be Banach spaces and let be closed operator ideals. Let be a Banach space having the Radon-Nikodým property. The main results are as follows. If is a Hahn-Banach extension operator, then there exists a set of Hahn-Banach extension operators , , such that , where . If is an ideal in for all equivalently renormed versions of , then there exist Hahn-Banach extension operators and such that .
3.
Hsien-Chung Wu 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(1):469-477
The conventional Hahn-Banach extension theorem based on vector space has been widely used to obtain many important and interesting results in nonlinear analysis, vector optimization and mathematical economics. Although the interval space is not a real vector space, the Hahn-Banach extension theorems based on interval spaces and nonstandard normed interval spaces can still be derived in this paper, which also shows the possible applications by considering the interval-valued problems in nonlinear analysis, vector optimization and mathematical economics. 相似文献
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5.
Abel群上的Hahn-Banach定理 总被引:1,自引:1,他引:0
进一步研究了可换平移空间与次范整线性空间之间的关系,建立了Abel群上的Hahn-Banach定理,作为其推论,得到了次范整线性空间中的Hahn-Banach定理. 相似文献
6.
B.L. Chalmers M.I. Ostrovskii B. Shekhtman 《Journal of Computational Analysis and Applications》2003,5(1):11-24
In this paper we review ongoing work on operators having norm-preserving extensions to every overspace. We call them Hahn-Banach operators. 相似文献
7.
H. Jarchow C. Palazuelos D. Pérez-García I. Villanueva 《Journal of Mathematical Analysis and Applications》2007,336(2):1161-1177
The aim of this paper is to investigate close relations between the validity of Hahn-Banach extension theorems for multilinear forms on Banach spaces and summability properties of sequences from these spaces. A case of particular importance occurs when we consider Banach spaces which have the property that every bilinear form extends to any superspace. 相似文献
8.
经典的Hahn-Banach定理告诉读者在有界映射空间(B(·,·),‖·‖)中C具有内射性.在第二节中主要研究在原子映射空间(NB(·,·),vB)中的内射性.作者得到任意有限维Banach空间在原子映射空间(NB(·,),vB)中都是内射的.这可以看作(NB(·,·),vB)中的广义Hahn-Banach定理.在经典的Banach空间理论中,众所周知一个Banach空间E在(B(·,·),‖·‖)中具有{l1n}n∈N有限可表示性当且仅当E同构于某个超积∏l1(n(α))的子空间.作为第二节的一个应用,第三节中作者研究了在原子映射空间(NB(·,·),vB)中的{l1n}n∈N有限可表示性.作者得到C是唯一在原子映射空间(NB... 相似文献
9.
Vegard Lima 《Journal of Mathematical Analysis and Applications》2007,334(1):593-603
We study the weak metric approximation property introduced by Lima and Oja. We show that a Banach space X has the weak metric approximation property if and only if F(Y,X), the space of finite rank operators, is an ideal in W(Y,X∗∗), the space of weakly compact operators for all Banach spaces Y. 相似文献
10.
Let T~=i=1
n irvi:V V=[v1,. . . .,vn] X, where i V* and X is a Banach space. Let T= i=1
nuivi: X V be an extension of T~ to all of X (i.e., ui X*) such that T has minimal (operator) norm. (E.g., if T~=I, T is a minimal projection from X onto V.) Then it is necessary and sufficient that u:=u_1,. . . ,un is given by (v:=v1,. . . ,vn)extv(u) Vn,where the notion of a v-extremal (extv) of u is properly defined.The condition above leads in many important cases to a simple geometric interpretation of minimal projections. Furthermore, by applying this formula to the case X=Lp, we obtain a linear n-dimensional analog of the Hölder equality condition (M is given by extv(u)=Mv)1/p u · Mv = 1/q u · Mv,wherever v is differentiable.We point out several applications, including the determination of the absolute projection constant of
n
p
相似文献
11.
本文给出了关于L0- 线性函数的Hahn-Banach 扩张定理的几何形式并证明这个几何形式等价于它的代数形式. 进一步, 我们利用这个几何形式给出了随机局部凸模中熟知的基本分离定理的一个新的且简单的证明. 最后, 利用这个分离定理, 我们同时在两种拓扑 —(ε, λ)- 拓扑和局部L0- 凸拓扑下证明了随机赋范模中的Goldstine-Weston 稠密性定理, 并举出一个反例说明在局部L0- 凸拓扑下如果随机赋范模不具有可数连接性质, 则Goldstine-Weston 稠密性定理不一定成立. 相似文献
12.
基于概率测度理论基础,研究了随机赋范空间中算子随机范数,得到了线性算子空间与线性泛函的若干随机化结果与随机化的Hahn-Banach延拓定理.结果可能成为随机泛函分析与概率论及应用的理论工具. 相似文献
13.
Alain A. Lewis 《Mathematical Social Sciences》1990,20(3)
Let ΓX() = X, A (X), υ be a cooperative von Neumann game with side payments, where X is a nonempty set of arbitrary cardinality, A(X) the Boolean ring generated from P(X) with the operations Δ and ∩ for addition and multiplication, respectively, such that S2 =S for all S ε A (X), and
with ;() = 0. The Shapley-Bondareva-Schmeidler Theorem, which states that a game of the form ΓX() = X, A (X), is weak if and only if the core of ΓX(),ζ(ΓX()), is normal, may be regarded as the fundamental theorem for weak cooperative games with side-payments. In this paper we use an ultrapower construction on the reals,
, to summarize a common mathematical theme employed in various constructions used to establish the Shapley-Bondareva-Schmeidler Theorem in the literature (Dalbaen, 1974; Kannai, 1969; Schmeidler, 1967, 1972). This common mathematical theme is that the space L, comprised of finite, real linear combinations of the collection of functions, {χa : a ε A (X)}, possesses a certain extension property that is intimately related to the Hahn-Banach Theorem of functional analysis. A close inspection of the extension property reveals that the Shapley-Bondareva-Schmeidler Theorem is in fact equivalent to the Hahn-Banach Theorem. 相似文献
14.
We work in set theory ZF without axiom of choice. Though the Hahn-Banach theorem cannot be proved in ZF, we prove that every Gateaux-differentiable uniformly convex Banach space E satisfies the following continuous Hahn-Banach property: if p is a continuous sublinear functional on E, if F is a subspace of E, and if f: F → ? is a linear functional such that f ≤ p|F then there exists a linear functional g : E → ? such that g extends f and g ≤ p. We also prove that the continuous Hahn-Banach property on a topological vector space E is equivalent to the classical geometrical forms of the Hahn-Banach theorem on E. We then prove that the axiom of Dependent choices DC is equivalent to Ekeland's variational principle, and that it implies the continuous Hahn-Banach property on Gateaux-differentiable Banach spaces. Finally, we prove that, though separable normed spaces satisfy the continuous Hahn-Banach property, they do not satisfy the whole Hahn-Banach property in ZF+DC. 相似文献
15.
Pei-Kee Lin 《数学学报(英文版)》2008,24(5):877-880
We prove that every 2-homogeneous polynomial on the complex co has a unique normpreserving extension to its bidual l∞. 相似文献
16.
Let X be a Banach space. We give characterizations of when is a u-ideal in for every Banach space Y in terms of nets of finite rank operators approximating weakly compact operators. Similar characterizations are given for
the cases when is a u-ideal in for every Banach space Y, when is a u-ideal in for every Banach space Y, and when is a u-ideal in for every Banach space Y. 相似文献
17.
Seppo Hassi Adrian Sandovici Henk de Snoo Henrik Winkler 《Acta Mathematica Hungarica》2006,111(1-2):81-105
Summary The sum of two unbounded nonnegative selfadjoint operators is a nonnegative operator which is not necessarily densely defined.
In general its selfadjoint extensions exist in the sense of linear relations (multivalued operators). One of its nonnegative
selfadjoint extensions is constructed via the form sum associated with A and B. Its relations to the Friedrichs and Krein--von Neumann extensions of A+Bare investigated. For this purpose, the one-to-one correspondence between densely defined closed semibounded forms and semibounded
selfadjoint operators is extended to the case of nondensely defined semibounded forms by replacing semibounded selfadjoint
operators by semibounded selfadjoint relations. In particular, the inequality between two closed nonnegative forms is shown
to be equivalent to a similar inequality between the corresponding nonnegative selfadjoint relations.</o:p> 相似文献
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19.
B.P. Duggal 《Journal of Mathematical Analysis and Applications》2007,335(2):990-995
Necessary and sufficient conditions for hypercyclic/supercyclic Banach space operators T to satisfy are proved. 相似文献
20.
Witold Majdak Zoltá n Sebestyé n Jan Stochel James E. Thomson 《Proceedings of the American Mathematical Society》2006,134(6):1687-1699
Criteria for the existence of lifts of operators intertwining subnormal operators are established. The main result of the paper reduces lifting questions for general subnormal operators to questions about lifts of cyclic subnormal operators. It is shown that in general the existence of local lifts (i.e. those coming from cyclic parts) for a pair of subnormal operators does not imply the existence of a global lift. However this is the case when minimal normal extensions of subnormal operators in question are star-cyclic.