共查询到20条相似文献,搜索用时 140 毫秒
1.
本文研究了Banach空间的弱*序列紧性,Banach空间X称为有(ω)性质,如果X’(X的共轭空间)的每个有界序列有弱*收敛子列,我们证明了,如果Banach空间X有(ω)性质,那么lp(X)(1≤p< ∞)与c0(X)也有(ω)性质。 相似文献
2.
设X是桶空间,Y是序列完备的局部凸空间.本文证明了,由X到Y的紧算子组成的算子级数,其在弱算子拓扑下和一致算子拓扑下的子级数收敛是一致的,当且仅当(X’,β(X’,X))不拓扑同胚地包含CO;同时证明了,N’中σ(X’,X)-子级数收敛级数是β(X’;X)-子级数收敛的,当且仅当(X’,β(X’,X))不拓扑同胚地包含CO. 相似文献
3.
4.
5.
关于Banach空间中Lipschitz强伪压缩映象的带误差的Ishikawa型迭代序列 总被引:19,自引:0,他引:19
设X是任意实B&nach空间E的闭子空间,TX→X是Lipschitz强伪压缩映象,使得Tx*=x*,对某x*∈X…在没有条件limαn=nlimβn=0之下,本文证明了带误差的Ishikawa型迭代序列强收敛到x*.另外,相关结果又证明了,当TE→E是Lipschitz强增生算子时,带误差的Ishikawa型迭代序列强收敛到方程Tx=f的唯一解. 相似文献
6.
林静玲林福财 《数学的实践与认识》2022,(9):168-174
设X是Hausdorff拓扑空间,超空间S(X)中的每一元素是X中有限个收敛序列的并且赋予Vietoris拓扑.主要讨论当空间X分别是序列连通、道路连通和c半层空间,则超空间S(X)是否分别是序列连通、道路连通和c半层空间.对这些问题给出(部分)回答. 相似文献
7.
本文引入了一个广义的约当-冯诺依曼型常数,并研究了它的相关性质,同时还利用广义的约当-冯诺依曼型常数,弱正交系数μ(X)和Domínguez-Benavides系数R(1,X),对Banach空间中的弱收敛序列系数WCS(X)进行了估计,从而得到了空间具有正规结构的一些充分条件.这些结论严格推广了最近一些文献中的结果. 相似文献
8.
证明了如下结果:(1)拓扑空间X具有局部可数弱基当且仅当X是度置空间的1-序列复盖商ss-映象;(2)拓扑空间X具有局部可数基当且仅当X是度量空间的2-序列复盖商ss-映象。 相似文献
9.
10.
集值条件期望的一个Fatou型引理 总被引:4,自引:0,他引:4
本文讨论了Banach空间只订合序列弱收敛的一些性质,给出了集值条件期望的表示定量,证明了集值条件期望在弱收敛意义下的Fatou型引理和控制收敛定理,并由此得到了一个可积选择空间的收敛定理。 相似文献
11.
Z. Kh. Zakirova 《Theoretical and Mathematical Physics》2018,196(1):965-975
We study n-dimensional pseudo-Riemannian spaces Vn(gij) with an arbitrary signature that admit projective motions, i.e., groups of continuous transformations preserving geodesics. In particular, we find the metric of a pseudo-Riemannian space of special type and establish important projective-group properties of this space. 相似文献
12.
A general Riesz merotopic space (X, ν) determines a not necessarily topological closure operator cν on X. The space (X, ν) is said to be complete if every cluster on (X, ν) is contained in an adherence grill on (X, cν). We discuss a method of obtaining a large class of completions of a given Riesz merotopic space with induced T1 closure space. As special cases we get the simple completion, which induces a simple closure space extension, and the strict completion, which induces a strict closure space extension. We show that the category of complete separated T1 Riesz merotopic spaces is epireflective in the category of separated T1 Riesz merotopic spaces, the reflection of an object being the simple completion. Similarly the category of complete clan-covered quasi-regular T1 Riesz merotopic spaces is epireflective in the category of clan-covered quasi-regular T1 Riesz merotopic spaces, the reflection of an object being the strict completion. 相似文献
13.
We consider the problem how far from being homotopy commutative is a loop space having the homotopy type of the p-completion of a product of finite numbers of spheres. We determine the homotopy nilpotency of those loop spaces as an answer
to this problem. 相似文献
14.
Georg Schumacher 《manuscripta mathematica》1985,50(1):229-267
We construct a Kähler metric on the moduli spaces of compact complex manifolds with c1,<0 and of polarized compact Kähler manifolds with c1=0, which is a generalization of the Petersson-Well metric. It is induced by the variation of the Kähler-Einstein metrics on the fibers that exist according to the Calabi-Yau theorem. We compute the above metric on the moduli spaces of polarized tori and symplectic manifolds. It turns out to be the Maaß metric on the Siegel upper half space and the Bergmann metric on a symmetric space of type III resp. In particular it is Kähler-Einstein with negative curvature.Dedicated to Karl SteinHeisenberg-Stipendiat der Deutschen Forschungsgemeinschaft 相似文献
15.
Takahisa Miyata 《Topology and its Applications》2012,159(3):921-932
The extension problem is to determine the extendability of a mapping defined on a closed subset of a space into a nice space such as a CW complex over the whole space. In this paper, we consider the extension problem when the codomains are general spaces. We take a shape theoretic approach to generalize the extension theory so that the codomains are allowed to be general spaces. We extend the notion of extension type which has been defined for the class of CW complexes and introduce the notion of approximate extension type which is defined for general spaces. We define approximate extension dimension analogously to extension dimension, replacing the class of CW complexes by the class of finitistic separable metrizable spaces. For every metrizable space X, we show the existence of approximate extension dimension of X. 相似文献
16.
Michael Ruzhansky 《Results in Mathematics》2003,44(1-2):159-168
17.
In this paper we study homotopical properties of a special neighborhood system, which is denoted by {Uε}?>0, for the canonical embedding of a compact metric space in its upper semifinite hyperspace to get results in the shape theory for compacta. We also point out that there are spaces with the shape of finite discrete spaces and having not the homotopy type of any T1-space 相似文献
18.
《Quaestiones Mathematicae》2013,36(4):359-374
Abstract Let (Z,Γ) be an H-structure. Then, for each exponential object Y in TOP, an H-structure is induced on the topological space Ct(Y,Z) of continuous maps equipped with the appropriate function space topology t (e.g. t = Tis, where Tis is the Isbell topology on C(Y,Z)). If (Z,Γ) is H-associative (resp.admits inversion), then the induced H-structure is also H-associative (resp. admits inversion). If (Z,Γ) is H-associative and admits inversion (e.g. a topological group) then all path components of Ct(Y,Z) belong to the same homotopy type. We also study the special case of (Z,Γ) being a topological group. Moreover, we prove that certain functions between function spaces are H-homomorphisms of the induced H-structures in the function spaces. 相似文献
19.
Denny H. Leung 《Mathematische Nachrichten》1990,149(1):177-181
We consider a Gelfand-Phillips type property for the weak topology. The main results that we obtain are (1) for certain Banach spaces, E?? F inherits this property from E and F, and (2) the spaces Lp(μ, E) have this property when E does. A subset A of a Banach space E is a limited set if every (bounded linear) operator T:E → c0 maps A onto a relatively compact subset of c0. The Banach space E has the Gelfand-Phillips property if every limited set is relatively compact. In this note, we study the analogous notions set in the weak topology. Thus we say that A ? E is a Grothendieck set if every T: E → c0 maps A onto a relatively weakly compact set; and E is said to have the weak type GP property if every Grothendieck set in E is relatively weakly compact. In the papers [3, 4 and 6], it is shown among other results that the ?-tensor product E and the spaces Lp(μ, E) inherit the Gelfand-Phillips property from E and F. In this paper, we study the same questions for the weak type GP property. It is easily verified that continuous linear images of Grothendieck sets are Grothendieck and that the weak type GP property is inherited by subspaces. Among the spaces with the weak type GP property one easily finds the separable spaces, and more generally, spaces with a weak* sequentially compact dual ball. Also, C(K) spaces where K is (DCSC) are weak type GP (see [3] and the discussion before Corollary 4 below). A Grothendieck space (a Banach space whose unit ball is a Grothendieck set) has the weak type GP if and only if it is reflexive. 相似文献
20.
Thomas Schott 《Mathematische Nachrichten》1998,189(1):221-242
In this paper we define weighted function spaces of type Bspq(u) and Fspq(u) on the Euclidean space IRn, where u is a weight function of at most exponential growth. In particular, u(x) = exp(±|χ|) is an admissible weight. We prove some basic properties of these spaces, such as completeness and density of the smooth functions. 相似文献