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1.
正规弱θ空间的无限Tychonoff积   总被引:1,自引:1,他引:0  
本文证明:(1)如果X=∏σ∈∑Xσ是|∑|-仿紧空间,则X是正规弱θ可加空间当且仅当?F∈[∑],∏σ∈FXσ是正规弱θ-可加空间.(2)设X=∏i∈ωXi是可效仿紧的,则下列三条等价:是正规弱θ-可加的;?F∈[ω],∏i∈FXi是正规弱θ-可加的;?n∈ω;∏i≤n  相似文献   

2.
吴畏 《中国科学A辑》2000,30(12):1081-1087
讨论在C*-凸理论下C*-代数A的广义态空间SCn(A)中的Krein-Milman型问题.证明了SCn(A)的任意一个BW-紧的C*-凸子集K都具有一个C*-端点,而且K是其C*-端点的C*-凸包.  相似文献   

3.
汪火云  卢建平 《数学研究》1999,32(4):393-397
引进了 σω(σκ)的定义 ,利用它刻划了 Fréchet空间 (κ′-空间 )的仿紧性 .主要结果是 :一个 Fréchet空间 (κ′-空间 )是仿紧的 它是正则的弱θ可加细空间且有性质σω(σκ)  相似文献   

4.
若φ 为单位圆盘D上的解析自映射, X为D上解析函数全体构成的Banach空间.定义X上复合算子Cφ: Cφ (f)=fοφ, 对任意 f∈X. 该文研究了从双曲α-Bloch 空间到双曲QK型空间上复合算子的有界性的特征. 另外, 还给出了从Dp,α 到QK(p, q) 空间上复合算子的有界性和紧性的特征.  相似文献   

5.
给出空间弱(K1, K2) -拟正则映射的定义, 并以Hodge分解及弱逆Hölder不等式为工具, 得到了其正则性结果:对任意满足 的q1, 都存在可积指数 使得对任意弱 (K1, K2) -拟正则映射 都有 即f为通常意义下的(K1, K2) -拟正则映射.  相似文献   

6.
设H(D) 表示单位圆盘D上的解析函数空间,u ∈ H(D). 该文研究了从混合模空间到Bloch -型空间微分算子与乘子的积DMu 的有界性与紧性.  相似文献   

7.
几个覆盖性质与分离性   总被引:5,自引:0,他引:5  
龙冰 《数学学报》1986,29(5):666-669
<正> 本文讨论了拟仿紧(狭义拟仿紧)、次拟仿紧(狭义次拟仿紧)、θ-可加细、弱θ-可加细以及弱θ-可加细空间等之间的关系.这些空间都是弱仿紧和次仿紧空间的弱化.联系上述覆盖性质,对[1]、[2]中的δ-集体正规性作了进一步探讨.对不可约空间也作  相似文献   

8.
曹金文 《数学杂志》2003,23(2):237-240
本文证明了如下结果:设X=lin←{Xσ,πρ^σ∧},|∧|=λ,并且每个投身πσ:X→Xσ是开满射,(a).若X是λ-仿紧的并且每个Xσ是正规弱δθ-可加空间,则X是正规弱δθ-可加空间;(b).若X是λ-仿紧的并且每个Xσ是遗传正规的遗传弱δθ-可加,则X是遗传正规的遗传弱δθ-可加空间。  相似文献   

9.
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   

10.
A是Woronowicz C*代数, G是作用于其上的离散群, 主要证明了它们的交叉积代数αG的正则表示和协变表示都对应于乘法酉算子,同时证明了正则协变的C*代数也是一个对应乘法酉算子的Woronowicz C*代数,最后给出了C(SUq(2)×αZ对应的乘法酉算子的一个明确表示.  相似文献   

11.
We show that the product of a subparacompact C-scattered space and a Lindelöf D-space is D. In addition, we show that every regular locally D-space which is the union of a finite collection of subparacompact spaces and metacompact spaces has the D-property. Also, we extend this result from the class of locally D-spaces to the wider class of D-scattered spaces. All the results are shown in a direct way.  相似文献   

12.
We show in a direct way that a space is D if it is a finite union of subparacompact scattered spaces. This result cannot be extended to countable unions, since it is known that there is a regular space which is a countable union of paracompact scattered spaces and which is not D. Nevertheless, we show that every space which is the union of countably many regular Lindelöf C-scattered spaces has the D-property. Also, we prove that a space is D if it is a locally finite union of regular Lindelöf C-scattered spaces.  相似文献   

13.
It is shown that the space Cp(τω) is a D-space for any ordinal number τ, where . This conclusion gives a positive answer to R.Z. Buzyakova's question. We also prove that another special example of Lindelöf space is a D-space. We discuss the D-property of spaces with point-countable weak bases. We prove that if a space X has a point-countable weak base, then X is a D-space. By this conclusion and one of T. Hoshina's conclusion, we have that if X is a countably compact space with a point-countable weak base, then X is a compact metrizable space. In the last part, we show that if a space X is a finite union of θ-refinable spaces, then X is a αD-space.  相似文献   

14.
In this note, we comment on D-spaces, linearly D-spaces and transitively D-spaces. We show that every meta-Lindelöf space is transitively D. If X is a weak -refinable TD-scattered space, then X is transitively D, where TD is the class of all transitively D-spaces. If X is a weak -refinable -scattered space, then X is a D-space, where is the class of all D-spaces, and hence every weak -refinable (or submetacompact) scattered space is a D-space. This gives a positive answer to a question mentioned by Martínez and Soukup. In the last part of this note, we show that if X is a weak -refinable space then X is linearly D.  相似文献   

15.
16.
We show that every regular T1 submeta-Lindelöf space of cardinality ω1 is D under MA+¬CH, which answers a question posed by Gruenhage (2011) [9]. Borges (1991) [5] asked if every monotonically normal paracompact space is a D-space, we give a characterization of paracompactness for monotonically normal spaces, which may be of some use in solving this problem.  相似文献   

17.
In this note, we show that if X is the union of a finite collection of strong Σ-spaces, then X is a D-space. As a corollary, we get a conclusion that if X is the union of a finite collection of Moore spaces, then X is a D-space. This gives a positive answer to one of Arhangel'skii's problems [A.V. Arhangel'skii, D-spaces and finite unions, Proc. AMS 132 (7) (2004) 2163-2170]. In the last part of the note, we show that if X is the union of a finite collection of DC-like spaces, then X is a D-space, where DC is the class of all discrete unions of compact spaces. As a corollary, we show that if X is the union of a finite collection of regular subparacompact C-scattered spaces, then X is a D-space.  相似文献   

18.
It is shown that (1) every infinite-dimensional Banach space admits aC 1 Lipschitz map onto any separable Banach space, and (2) if the dual of a separable Banach spaceX contains a normalized, weakly null Banach-Saks sequence, thenX admits aC map onto any separable Banach space. Subsequently, we generalize these results to mappings onto larger target spaces. Supported by an NSF Postdoctoral Fellowship in Mathematics.  相似文献   

19.
We introduce notions of nearly good relations and N-sticky modulo a relation as tools for proving that spaces are D-spaces. As a corollary to general results about such relations, we show that Cp(X) is hereditarily a D-space whenever X is a Lindelöf Σ-space. This answers a question of Matveev, and improves a result of Buzyakova, who proved the same result for X compact.We also prove that if a space X is the union of finitely many D-spaces, and has countable extent, then X is linearly Lindelöf. It follows that if X is in addition countably compact, then X must be compact. We also show that Corson compact spaces are hereditarily D-spaces. These last two results answer recent questions of Arhangel'skii. Finally, we answer a question of van Douwen by showing that a perfectly normal collectionwise-normal non-paracompact space constructed by R. Pol is a D-space.  相似文献   

20.
We introduce the classes of monotonically monolithic and strongly monotonically monolithic spaces. They turn out to be reasonably large and with some nice categorical properties. We prove, in particular, that any strongly monotonically monolithic countably compact space is metrizable and any monotonically monolithic space is a hereditary D-space. We show that some classes of monolithic spaces which were earlier proved to be contained in the class of D-spaces are monotonically monolithic. In particular, Cp(X) is monotonically monolithic for any Lindelöf Σ-space X. This gives a broader view of the results of Buzyakova and Gruenhage on hereditary D-property in function spaces.  相似文献   

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