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Banach空间中极大单调算子零点的迭代逼近定理 总被引:1,自引:0,他引:1
令E为实光滑、一致凸Banach空间,E为其对偶空间.令A■ E x E为极大单调算子, A-10≠■.本文将引入新的迭代算法,并利用Lyapunov泛函, Qr算子与广义投影算子等技巧,证明了迭代序列弱收敛于极大单调算子A的零点的结论. 相似文献
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Banach空间中极大单调算子零点的带误差项的新迭代格式 总被引:8,自引:0,他引:8
令E为实光滑、一致凸Banach空间,E为其对偶空间,AE×E为极大单调算子且A-10≠Φ.本文将引入新的迭代算法,并利用Lyapunov泛函,Qr算子与广义投影算子等技巧,证明了迭代序列弱收敛于极大单调算子A的零点的结论. 相似文献
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定义了一类极大外平面图:(r,k)--扇。证明了当G是以r个顶点的圈Qr为标定界环的(r,k)一扇,G'是以Qr为标定界环的任意极大外平面图时,G和G'有公共四染色;同时对△(G)=r-3的极大外平在图也得到相同的结论。从而证明了四色定理的等价命题在给定条件下成立。 相似文献
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本文回答了关于MCM空间遗传性的一个问题,讨论了k-MCM空间是k半层空间的条件,得到了一些用g函数刻划的度量化定理.主要结论有:MCM空间是关于Fσ子空间遗传的;在正规空间类中,q空间(ωN空间,k-MCM空间)是关于开Fσ子空间遗传的;如果X是具有Gδ对角线的正则次中紧 k-MCM空间,则X是k半层空间;X是可度量化空间的充要条件是存在X上的g函数满足对X中任意不相交的闭集F与紧集C,都有某个n∈ω,使得(∪x∈F g(n,x))∩(∪y∈C g(n,y))=(?). 相似文献
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证明了在扩大的非标准模型中S-空间可完全表示Radon空间并讨论了S-空间的若干性质.还给出一个有限Borel测度空间为Radon空间的充要条件.最后证明了Radon空间的一个*-有限表示定理. 相似文献
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引入了两个很有联系的空间类JHB-空间与强J HB-空间,分别推广了J-空间与强J-空间.讨论了J-空间、强J-空间、J HB-空间及强JHB-空间类间的相包含关系及此四空间类逆包含的条件,还得到了JHB-空间的内部刻画,并证明了若对每个α∈S,Xα.都是非紧的连通空间,则积空间∏α∈S Xα是强J-空间。 相似文献
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大家知道,空间是物质存在的普遍形式。现实世界中的万事万物无不存在于空间之中,并在其中运动、变化和发展。这种现实的空间就是数学中所研究的三维欧氏空间。十九世纪以前的数学都是在这种三维欧式空间中讨论的,二维空间(平面)与一维空间(直线)是它的特殊情况。从十九世纪中叶开始,数学家在数学研究中引入了高于三维的多维空间,并建立了多维空间的几何学。进入二十世纪以后,数学中讨论着各种各样的“空间”,从有限维的到无限维的,既然现实的空间是三维的,为什么要引入多维甚至无限维的空间呢,它们是怎样产生的,又有什么现实… 相似文献
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L—FUZZY拓扑空间中几种紧性 总被引:1,自引:1,他引:0
本文在L-fuzzy拓扑空间中引进了几种不同的具有有限交性质的闭集族,并以此刻划了良紧空间、强F紧空间和F紧空间的特征。另外,对F紧空间还给出了复盖式以及远域族式的刻划。 相似文献
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具有σ局部有限sn网的正则空间称为sn可度量化空间,本文讨论了k半层空间的可扩性质,证明了序列覆盖的闭映射保持sn可度量化空间,同时给出与sn可度量化空间的映射性质相关的几个例子。 相似文献
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本文给出了一个关于半自反infra-(u)空间的闭图定理.作为推论,证明了从速完备 Mazur空间到半自反infra-(u)空间的闭图线性映照为弱连续、Mackey连续和强连续的. 相似文献
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Andreas Kollross 《Transactions of the American Mathematical Society》2002,354(2):571-612
An isometric action of a compact Lie group on a Riemannian manifold is called hyperpolar if there exists a closed, connected submanifold that is flat in the induced metric and meets all orbits orthogonally. In this article, a classification of hyperpolar actions on the irreducible Riemannian symmetric spaces of compact type is given. Since on these symmetric spaces actions of cohomogeneity one are hyperpolar, i.e. normal geodesics are closed, we obtain a classification of the homogeneous hypersurfaces in these spaces by computing the cohomogeneity for all hyperpolar actions. This result implies a classification of the cohomogeneity one actions on compact strongly isotropy irreducible homogeneous spaces.
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Tepper L. Gill Sudeshna Basu Woodford W. Zachary V. Steadman 《Proceedings of the American Mathematical Society》2004,132(5):1429-1434
In this paper we show that a result of Gross and Kuelbs, used to study Gaussian measures on Banach spaces, makes it possible to construct an adjoint for operators on separable Banach spaces. This result is used to extend well-known theorems of von Neumann and Lax. We also partially solve an open problem on the existence of a Markushevich basis with unit norm and prove that all closed densely defined linear operators on a separable Banach space can be approximated by bounded operators. This last result extends a theorem of Kaufman for Hilbert spaces and allows us to define a new metric for closed densely defined linear operators on Banach spaces. As an application, we obtain a generalization of the Yosida approximator for semigroups of operators.
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David Pierce 《Archive for Mathematical Logic》2009,48(5):421-436
Vector spaces over unspecified fields can be axiomatized as one-sorted structures, namely, abelian groups with the relation
of parallelism. Parallelism is binary linear dependence. When equipped with the n-ary relation of linear dependence for some positive integer n, a vector-space is existentially closed if and only if it is n-dimensional over an algebraically closed field. In the signature with an n-ary predicate for linear dependence for each positive integer n, the theory of infinite-dimensional vector spaces over algebraically closed fields is the model-completion of the theory
of vector spaces.
相似文献
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Mehmet Baran 《Applied Categorical Structures》2002,10(4):403-415
In this paper, the characterization of closed and strongly closed subobjects of an object in categories of various types of filter convergence spaces is given and it is shown that they induce a notion of closure. Furthermore, each of the notions of compactness, perfectness, separation, minimality and absolute closedness with respect to these two new closure operators are characterized in these categories and some known results are re-obtained. 相似文献
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林寿 《数学年刊A辑(中文版)》2017,38(3):269-276
箱积中正规性或仿紧性的研究是一般拓扑学中极其困难的问题.作者以紧有限闭扩张和定理为基础,建立了一个广义度量空间类的箱积定理,由此导出k~*可度量空间及具有点可数k网的空间等均关于箱积运算保持. 相似文献
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A note on closed images of locally compact metric spaces 总被引:1,自引:0,他引:1
Shou Lin 《Acta Mathematica Hungarica》2005,109(1-2):157-162
Summary A decomposition theorem about closed images of locally compact metric spaces is discussed. It is shown that a space is a closed
image of a locally compact metric space if and only if it is a regular Fréchet space with a point-countable k-network, and each of its closed first-countable subset is locally compact. 相似文献
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We prove a multiplicity one theorem for the length spectrum of compact even dimensional hyperbolic spaces, i.e., if all but finitely many closed geodesics for two compact even dimensional hyperbolic spaces have the same length, then all closed geodesics have the same length. 相似文献