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 共查询到19条相似文献,搜索用时 125 毫秒
1.
本文研究了弱(序列式)紧正则诱导极限与凸弱(序列式)紧正则诱导极限.满足Retakh条件(M0)的(LF)-空间必为凸弱(序列式)紧正则的,但未必为弱(序列式)紧正则的.对于弱序列式完备Frechet空间的可数诱导极限,Retakh条件(M0)蕴涵弱(序列式)紧正则性.特别地,对于Kothe(LF)-序列空间Ep(1≤p<∞),Retakh条件(M0)等价于弱(序列式)紧正则性.对于这类空间,利用Vogt的有关结论,给出了弱(序列式)紧正则性的特征.  相似文献   

2.
丘京辉 《数学学报》2006,49(6):1231-123
本文研究Retakh's条件(M_0),正则性和弱序列式回缩性之间的关系.对于(LM)-空间,弱序列式回缩性等价于正则性加上一个介于(Q_0)和(M_0)之间的条件对于(LN)-空间,我们获得了更满意的结果,证明了弱序列式回缩性等价于正则性加上条件(M_0),也等价于一个非常弱的正则性条件加上条件(M_0)(见文献[1-28]).  相似文献   

3.
本文研究了诱导极限按弱拓扑的正则性.应用Banach圆盘的方法和严格网状空间的局部化定理,证明了若严格网状空间的诱导极限满足条件(Q0),则它必为凸弱可数紧正则的.  相似文献   

4.
证明了正则空间中闭Lindelof映射逆保持序列式meso紧性,从而改进了Mancuso V J关于正则空间中完备映射逆保持meso紧性这一结果;进一步我们指出定理条件中原象空间的正则性不可被省略而象空间的正则性可以用原象空间的正规性来替代.  相似文献   

5.
曾六川 《数学年刊A辑》2002,23(6):699-706
设X是p一致凸Banach空间,具有弱一致正规结构与非严格的Opial性质.又设C是X的非空凸弱紧子集.在适当的条件下,证明了C上每个渐近正则半群T={T(t)t∈S}都有不动点.进一步,在类似的条件下,也讨论了一致凸Banach空间中渐近正则半群的不动点的存在性.  相似文献   

6.
设X是p一致凸Banach空间,具有弱一致正规结构与非严格的Opial性质.又设C是X的非空凸弱紧子集.在适当的条件下,证明了C上每个渐近正则半群T={T(t):t∈S}都有不动点进一步,在类似的条件下,也讨论了一致凸Banach空间中渐近正则半群的不动点的存在性.  相似文献   

7.
丘京辉  QIU Jing-hui 《数学学报》2000,43(6):1105-111
本文研究了(LM)-空间(即:可尺度局部凸空间序列的诱导极限)中,Re-takh’s条件(M)与序列式回缩性之间的关系,给出了满足Retakh’s条件(M)的(LM)-空间为序列式回缩的一系列特征条件.  相似文献   

8.
研究了退化弱(k1,k2)拟正则映射的正则性.利用H lder不等式、Sobolev空间的空间分析方法,以及内插定理等工具,给出了退化弱(k1,k2)拟正则映射事实上为退化(k1,k2)拟正则映射的一个充分条件,其结果对非退化情形也成立.  相似文献   

9.
(弱)诱导空间的r连通性   总被引:1,自引:0,他引:1  
本文研究了分明拓扑空间与其诱导空间,弱诱导空间与其底空间之间的关系.利用LF-r开集定义了r连通性,得出了弱诱导的LF拓扑空间是r连通的当且仅当其底空间是r连通的,并且分析(弱)诱导空间的结构.  相似文献   

10.
方进明 《数学年刊A辑》2000,21(5):585-590
本文引入极小正则LF拓扑空间的概念,给出了构造弱于已知正则LF拓扑的正则LF拓扑的一般方法.此外,得出了正则LF拓扑成为极小正则LF拓扑的条件.  相似文献   

11.
A notion of an almost regular inductive limits is introduced. Every sequentially complete inductive limit of arbitrary locally convex spaces is almost regular.  相似文献   

12.
13.
Modifying the method of Ansari, we give some criteria for hypercyclicity of quasi-Mazur spaces. They can be applied to judging hypercyclicity of non-complete and non-metrizable locally convex spaces. For some special locally convex spaces, for example, Köthe (LF)-sequence spaces and countable inductive limits of quasi-Mazur spaces, we investigate their hypercyclicity. As we see, bounded biorthogonal systems play an important role in the construction of Ansari. Moreover, we obtain characteristic conditions respectively for locally convex spaces having bounded sequences with dense linear spans and for locally convex spaces having bounded absorbing sets, which are useful in judging the existence of bounded biorthogonal systems.  相似文献   

14.
It is shown that in Banach spaces with the property (M) of Kalton, nonexpansive self mappings of nonempty weakly compact convex sets necessarily have fixed points. The stability of this conclusion under renormings is examined and conditions for such spaces to have weak normal structure are considered.

  相似文献   


15.
This paper is concerned with some questions of regularity in increasing inductive sequences of locally convex spaces. It is shown that the various stronger terms of regularity coincide in case of normed steps and are equivalent with property (M) defined by Retakh which turned out to be basical in the topology problem of a subspace and well-location. Some of these results keep validity even in more general cases. Finally, an example of a regular but not sequentially-retractive (LB)-space is given answering some open related questions as well.  相似文献   

16.
本文首先通过暴露集和暴露泛函的概念引入了闭凸集的紧-严格凸、紧-强凸、紧-一致凸及紧-非常凸等概念。并用对偶映射给出了Banach空间的两种新光滑性—紧-一致光滑与紧-非常光滑。然后特别研究了Banach空间的紧-非常凸与紧-非常光滑。此外还得到关于对偶映射的两个新结果。  相似文献   

17.
Grothendieck asked in 1954 in [1] the following questions. (1) Is the bidual of a strict inductive limit of a sequence of locally convex spaces the inductive limit of the biduals? (2) Is the bidual of a strict (LF)-space again an (LF)-space? (3) Is the bidual of a strict (LF)-space complete? M. Valdivia gave a (negative) answer to the first question in 1979 in [5]. Since his counterexample is not an (LF)-space, problem (2) remained open. The aim of this note is to present a negative solution to questions (2) and (3). The answer to question (2) is negative even if every step of the (LF)-space is distinguished, in which case the strong bidual is complete by a result of Grothendieck. Moreover, we show that the strong dual of a strict (LF)-space need not be countably barrelled.  相似文献   

18.
We prove that a topological space is uniform Eberlein compact iff it is homeomorphic to a super weakly compact subset C of a Banach space such that the closed convex hull coC of C is super weakly compact. We also show that a Banach space X is super weakly compactly generated iff the dual unit ball BX* of X* in its weak star topology is affinely homeomorphic to a super weakly compactly convex subset of a Banach space.  相似文献   

19.
Countable projective spectra of countable inductive limits, called (PLB)-spaces, of weighted Banach spaces of continuous functions are investigated. It is characterized when the derived projective limit functor vanishes in terms of the sequences of the weights defining the spaces. The locally convex properties of the corresponding projective limits are analyzed, too. Received: 30 January 2009  相似文献   

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