共查询到19条相似文献,搜索用时 140 毫秒
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Geng Zhibin 《大学数学》1998,(2)
本文研究了Banach空间的弱序列紧性.Banach空间X称为有(w)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(w)性质,那么lp(X)(1≤p<+∞)与c0(X)也有(w)性质. 相似文献
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弱Herz空间的应用 总被引:27,自引:6,他引:21
设1〈q〈∞和0〈p≤1,本文证明了一大类算子有界地映Herz空间Kq^n(1-1/q,^p(R^n)到弱Herz空间WKq^n(1-1/q),^p(R^n)。本文还引入了弱Herz型Hardy空间,并且证明了局部Calderon-Zygmund型算子有界地映Herz型Hardy空间到弱Herz型Hardy空间。 相似文献
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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
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以R.Lowen的强F紧性为基础,定义了L-拓扑空间的弱局部强F紧性及单点强F紧化,推广了有关弱局部紧拓扑空间和拓扑空间的单点紧化的若干结果,证明了L-拓扑空间的弱局部强F紧性是拓扑空间的弱局部紧性的L-推广。 相似文献
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给出了一般的L-不分明拓扑空间的Alexandorff紧化,并且对弱诱导空间证明了该紧化是弱诱导紧化类中唯一最小的紧化。 相似文献
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X是Banach空间,对X的每一弱可分且弱紧的子集K,若(k,ω)可度量,则称X是次可分的。如果对任意的可分,则称X是拟可分的。本文证明了这两类新引入的空间比可分空间与弱紧生成的Banach空间都要广泛并且保留了可分空间的许多重要性质。 相似文献
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称局部凸空间(E,(?)0)为WCM空间若对于任何弱于(?)0的局部凸拓扑(?),(E,(?))与(E,(?)0)具相同的弱紧圆凸集.本文研究了WCM空间的存在性及其与其他类型局部凸空间之间的关系,还给出了WCM空间的一种映照特征. 相似文献
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Xi Cheng ZHANG 《数学学报(英文版)》2005,21(4):819-822
In this note, we obtain a sufficient and necessary condition for a set in an abstract Winner space (X, H, μ) to be relatively compact in L^2(X, μ). Meanwhile, we give a sufficient condition for relative compactness in L^P(X, μ) for p〉1. We also provide an example of Da Prato-Malliavin Nualart to show the result. 相似文献
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Based on an application of the Davis-Figiel-Johnson-Pelzyski procedure, this note shows that every weakly compact subset of a Banach space can be uniformly embedded into a reflexive Banach space. As its application, we present the recent renorming theorems for reflexive spaces of Odell- Schlumprecht and Hajek-Johanis can be extended and localized to weakly compact convex subsets of an arbitrary Banach space. 相似文献
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本文研究Banach空间X中远达和同时远达问题的适定性,在集合的Haus- dorff距离下,对X中的闭凸子集D和相对弱紧的有界闭子集K,证明了下述结果: 若D关于K严格凸和有Kadec性质,则D中所有使远达问题 max{x,K}是适定的 点x全体在D中是Gδ型集.作为应用,得到了同时远达问题适定性的类似结果. 相似文献
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The concept of locally strong compactness on domains is generalized to general topological spaces. It is proved that for each distributive hypercontinuous lattice L, the space SpecL of nonunit prime elements endowed with the hull-kernel topology is locally strongly compact, and for each locally strongly compact space X, the complete lattice of all open sets O(X) is distributive hypercontinuous. For the case of distributive hyperalgebraic lattices, the similar result is given. For a sober space X, it is shown that there is an order reversing isomorphism between the set of upper-open filters of the lattice O(X) of open subsets of X and the set of strongly compact saturated subsets of X, which is analogous to the well-known Hofmann-Mislove Theorem. 相似文献
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Jing Hui QIU 《数学学报(英文版)》2007,23(12):2295-2302
In the framework of topological vector spaces, we give a characterization of strong Minkowski separation, introduced by Cheng, et al., in terms of convex body separation. From this, several results on strong Minkowski separation are deduced. Using the results, we prove a drop theorem involving weakly countably compact sets in locally convex spaces. Moreover, we introduce the notion of the co-drop property and show that every weakly countably compact set has the co-drop property. If the underlying locally convex space is quasi-complete, then a bounded weakly closed set has the co-drop property if and only if it is weakly countably compact. 相似文献
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局部强紧空间的Hoare空间与Smyth空间 总被引:1,自引:0,他引:1
本文主要讨论局部强紧空间的性质,特别是其Hoare空间和Smyth空间的性质,证明了T_0空间为局部强紧空间的当且仅当其Hoare空间为局部强紧空间,局部强紧空间的Smyth空间为C-空间.对于强局部紧空间,我们有类似的结论. 相似文献
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倪仁兴 《数学物理学报(A辑)》2003,23(2):161-168
设C是实Banach空间X中有界闭凸子集且0是C的内点,G是X中非空闭的有界相对弱紧子集.记K(X)为X的非空紧凸子集全体并赋Hausdorff距离,KG(X)为集合{A∈K(X);A∩G=}的闭包.称广义共同逼近问题minC(A,G)是适定的是指它有唯一解(x0,z0),且它的每个极小化序列均强收敛到(x0,z0).在C是严格凸和Kadec的假定下,证明了{A∈K(X);minC(A,G)是适定的}含有KG(X)中稠Gδ子集,这本质地推广和延拓了包括De Blasi,Myjak and Papini[1]、Li[2]和De Blasi and Myjak[3]等人在内的近期相应结果. 相似文献
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It is shown that the space X[0,1], of continuous maps [0,1]X with the compact-open topology, is not locally compact for any space X having a nonconstant path of closed points. For a T1-space X, it follows that X[0,1] is locally compact if and only if X is locally compact and totally path-disconnected.
Mathematics Subject Classifications (2000) 54C35, 54E45, 55P35, 18B30, 18D15. 相似文献
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H. P. A. Künzi S. Romaguera M. A. Sánchez-Granero 《Czechoslovak Mathematical Journal》2004,54(1):215-228
We characterize those Tychonoff quasi-uniform spaces
for which the Hausdorff-Bourbaki quasi-uniformity is uniformly locally compact on the family
of nonempty compact subsets of X. We deduce, among other results, that the Hausdorff-Bourbaki quasi-uniformity of the locally finite quasi-uniformity of a Tychonoff space Xis uniformly locally compact on
if and only if Xis paracompact and locally compact. We also introduce the notion of a co-uniformly locally compact quasi-uniform space and show that a Hausdorff topological space is -compact if and only if its (lower) semi-continuous quasi-uniformity is co-uniformly locally compact. A characterization of those Hausdorff quasi-uniform spaces
for which the Hausdorff-Bourbaki quasi-uniformity is co-uniformly locally compact on
is obtained. 相似文献