Orlicz空间的若干紧一致凸性和k-drop凸性

给出赋Luxemburg范数的Orlicz函数空间的紧一致凸、弱紧一致凸、紧局部一致凸、弱紧局部一致凸和k-drop凸的判据,并且据此得到在Orlicz函数空间中这些凸性的等价关系.     

Topological Representations of Distributive Hypercontinuous Lattices

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.     

Invariant Sobolev Calculus on the Free Loop Space

We give integration by parts formulas over the free loop space of a compact riemannian manifold, after discussing the tangent space. We give a Sobolev Calculus based upon the H-derivative, after introducing some connections. We define an invariant by rotation Ornstein–Ühlenbeck operator over it. Some examples of smooth functionals are studied.     

Monotone retractability and retractional skeletons

We prove that a countably compact space is monotonically retractable if and only if it has a full retractional skeleton. In particular, a compact space is monotonically retractable if and only if it is Corson. This gives an answer to a question of R. Rojas-Hernández and V.V. Tkachuk. Further, we apply this result to characterize retractional skeleton using a topology on the space of continuous functions, answering thus a question of the first author and a related question of W. Kubi?.     

Weaker connected and weaker nowhere locally compact topologies for metrizable and similar spaces

We prove that any metrizable non-compact space has a weaker metrizable nowhere locally compact topology. As a consequence, any metrizable non-compact space has a weaker Hausdorff connected topology. The same is established for any Hausdorff space X with a σ-locally finite base whose weight w(X) is a successor cardinal.     

Embeddable quantum homogeneous spaces

We discuss various notions generalizing the concept of a homogeneous space to the setting of locally compact quantum groups. On the von Neumann algebra level we recall an interesting duality for such objects studied earlier by M. Izumi, R. Longo, S. Popa for compact Kac algebras and by M. Enock in the general case of locally compact quantum groups. A definition of a quantum homogeneous space is proposed along the lines of the pioneering work of Vaes on induction and imprimitivity for locally compact quantum groups. The concept of an embeddable quantum homogeneous space is selected and discussed in detail as it seems to be the natural candidate for the quantum analog of classical homogeneous spaces. Among various examples we single out the quantum analog of the quotient of the Cartesian product of a quantum group with itself by the diagonal subgroup, analogs of quotients by compact subgroups as well as quantum analogs of trivial principal bundles. The former turns out to be an interesting application of the duality mentioned above.     

Operations on approximatively compact sets

In the paper, the problem of preserving the property of approximative compactness under diverse operations is considered. In an arbitrary uniformly convex separable space, we construct an example of two approximatively compact sets whose intersection is not approximatively compact. An example of two linear approximatively compact sets for which the closure of their algebraic sum is not approximatively compact is constructed. In an arbitrary Banach space, we construct two nonlinear approximatively compact sets whose algebraic sum is closed but not approximatively compact. We also prove that any uniformly closed Banach space contains an approximatively compact cavity.     

局部强紧空间的Hoare空间与Smyth空间

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.     

An algebraic version of Tamano's theorem for countably compact spaces

We show that if X is countably compact but not compact then one can find a compact space K such that X⊕K does not embed closedly into any normal topological group.     

Dirichlet空间上的Bergman型Toeplitz算子

本文给出了Dirichlet空间上以有界调和函数为符号的Bergman型Toeplitz算子是紧算子的充要条件.同时刻画了此类Bergman型Toeplitz算子在Dirichlet空间上的交换性.     

关于M-PN空间中的非线性算子

在Menger概率线性赋范空间中,利用该空间中的Leray-Schauder拓扑度理论,研究非线性算子T,建立了紧连续算子了T有固有值γ和δW上存在对应于γ的固有元的一系列充分条件．同时,也改进和推广了若干个重要结论。     

The Law of the Iterated Logarithm for Weakly Dependent Hilbert Space Valued Random Variables

We consider the bounded and compact laws of the iterated logarithm for weakly dependent Hilbert space valued random variables. Under optimal moment conditions, we prove the bounded and compact laws of the iterated logarithm for sequences of identically distributed Hilbert space valued random variables satisfying the uniform strong mixing condition.     

某些局部凸空间上相对弱紧集，相对弱列紧集，相对弱可数紧集的关系

对可分离的局部凸空间（Ｘ，τ），本文建立了相应的局部凸空间（Ｑｘ，Ｔｘ），利用它证明了当（Ｘ，τ）满足某些条件时（赋范空间满足这些条件），ＥＸ相对弱紧Ｅ相对弱列紧Ｅ相对弱可数紧，从而推广了Ｅｂｅｒｌｅｉｎ等人的工作，证明了在空间Ｄ（Ｒ￣ｎ），（Ｒ￣ｎ）和Ｄ＿（ＬＰ），１＜ｐ＜∞上前述三种弱紧性等价．     

Locally Compact Path Spaces

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.     

Every weakly compact set can be uniformly embedded into a reflexive Banach space

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.     

A note on finite-sheeted covering maps from 2-dimensional compact Abelian groups

We consider finite-sheeted covering maps from 2-dimensional compact connected abelian groups to Klein bottle weak solenoidal spaces, metric continua which are not groups. We show that whenever a group covers a Klein bottle weak solenoidal space it covers groups as well, moreover it covers the product of two solenoids. The converse is not true, we give an example of group which covers groups with any finite number of sheets, but does not cover any Klein bottle weak solenoidal space.     

Banach空间中不适定线性算子方程的最佳逼近解

设X,Y为Banach空间,T为从X到Y的线性算子.T的值域R(T)≠Y且为逼近紧子空间,T的零空间N(T)≠{θ}.证得不适定算子方程Tx=y的最佳逼近解对任意y∈Y均存在的充分必要条件是N(T)为X的迫近子空间.     

Ideals of homogeneous polynomials and weakly compact approximation property in Banach spaces

We show that a Banach space E has the weakly compact approximation property if and only if each continuous Banach-valued polynomial on E can be uniformly approximated on compact sets by homogeneous polynomials which are members of the ideal of homogeneous polynomials generated by weakly compact linear operators. An analogous result is established also for the compact approximation property.     

Factorization theorems for cohomological dimension

The well-known factorization theorems for covering dimension dim and compact Hausdorff spaces are here established for the cohomological dimension dim using a new characterization of dim In particular, it is proved that every mapping f: X → Y from a compact Hausdorff space X with to a compact metric space Y admits a factorization f = hg, where g: X → Z, h: Z → Y and Z is a metric compactum with . These results are applied to the well-known open problem whether . It is shown that the problem has a positive answer for compact Hausdorff spaces X if and only if it has a positive answer for metric compacta X.     

弱紧局部一致凸空间中的度量投影

本文研究了弱紧局部一致凸空间中度量投影的弱连续性,将Ｂ．Ｂ．Ｐａｎｄａ和Ｏ．Ｐ．Ｋａｐｏｏｒ的相应结论推广到更一般的弱紧局部一致凸空间．最后给出了局部一致凸点的一个必要条件．