Eberlein mulian定理在局部凸空间中的推广

设（Ｅ，Ｔ）是一个分离的局部凸空间．本文主要结果是：（１）如果（Ｅ，Ｔ）是次可分的，那么ＡＥ是相对弱紧集Ａ是相对弱可数紧集Ａ是相对弱序列紧集．（２）如果（Ｅ，Ｔ）是强次可分且（Ｅ，β（Ｅ，Ｅ））是桶型空间，那么ＡＥ是相对弱紧集Ａ是相对弱可数紧集Ａ是相对弱序列紧集．     

Banach空间中远达和同时远达问题的适定性

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．     

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.     

局部有限超拓扑的局部紧性

本文讨论了赋予局部有限拓扑的非空闲子集超空间的局部紧性.主要结果是:X正则,则其闭子集超空间局部紧当且仅当X可表示成一个紧空间与一个离散空间的拓扑和.     

Uniform factorization for compact sets of operators

We prove a factorization result for relatively compact subsets of compact operators using the Bartle and Graves Selection Theorem, a characterization of relatively compact subsets of tensor products due to Grothendieck, and results of Figiel and Johnson on factorization of compact operators. A further proof, essentially based on the Banach-Dieudonné Theorem, is included. Our methods enable us to give an easier proof of a result of W.H. Graves and W.M. Ruess.

     

Relatively Compact Sets on Abstract Wiener Space

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.     

Relatively compact families of functionals on abstract Wiener space and applications

In this paper we prove two relatively compact criterions in some L^p-spaces(p>1) for the set of functionals on abstract Wiener space in terms of the compact embedding theorems in finite dimensional Sobolev spaces. Then, as applications we study several relatively compact families of random fields for the solutions to SDEs (and SPDEs) with coefficients satisfying some bounded assumptions, some stochastic integrals, and local times of diffusion processes.     

广义共同逼近问题的适定性

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minC(A,G)是适定的是指它有唯一解(x0,z0)，且它的每个极小化序列均强收敛到(x0,z0).在C是严格凸和Kadec的假定下，证明了｛A∈K(X)；minC(A，G)是适定的｝含有KG(X)中稠Gδ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.     

Polynomials and limited sets

We prove that scalar-valued polynomials are weakly continuous on limited sets and that, as in the case of linear mappings, every -valued polynomial maps limited sets into relatively compact ones. We also show that a scalar-valued polynomial whose derivative is limited is weakly sequentially continuous.

     

Indestructibility and stationary reflection

If κ < λ are such that κ is a strong cardinal whose strongness is indestructible under κ ‐strategically closed forcing and λ is weakly compact, then we show that A = {δ < κ | δ is a non‐weakly compact Mahlo cardinal which reflects stationary sets} must be unbounded in κ. This phenomenon, however, need not occur in a universe with relatively few large cardinals. In particular, we show how to construct a model where no cardinal is supercompact up to a Mahlo cardinal in which the least supercompact cardinal κ is also the least strongly compact cardinal, κ 's strongness is indestructible under κ ‐strategically closed forcing, κ 's supercompactness is indestructible under κ ‐directed closed forcing not adding any new subsets of κ, and δ is Mahlo and reflects stationary sets iff δ is weakly compact. In this model, no strong cardinal δ < κ is indestructible under δ ‐strategically closed forcing. It therefore follows that it is relatively consistent for the least strong cardinal κ whose strongness is indestructible under κ ‐strategically closed forcing to be the same as the least supercompact cardinal, which also has its supercompactness indestructible under κ ‐directed closed forcing not adding any new subsets of κ (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

非连续弱紧增算子的不动点及其对Banach空间初值问题的应用

证明了Banach空间上一类非连续的弱紧增算子的不动点定理,特别获得了最大不动点与最小不动点的存在性,改进了已有的某些结果.作为应用,讨论了Banach空间中含间断项的常微分方程初值问题最大解与最小解的存在性.     

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．     

Reduction of quasidifferentials and minimal representations

Some criterias for the non-minimality of pairs of compact convex sets of a real locally convex topological vector space are proved, based on a reduction technique via cutting planes and excision of compact convex subsets. Following an example of J. Grzybowski, we construct a class of equivalent minimal pairs of compact convex sets which are not connected by translations.Corresponding author.     

Some criteria for the minimality of pairs of compact convex sets

Some criteria for minimality for a pair of compact convex subsets of a real locally convex vector space are proved. Moreover several examples are given.     

Thermodynamic formalism for subadditive sequence of discontinuous functions

The topological pressure for subadditive sequence of discontinuous functions is defined on any invariant subset having a nested family of subsets in the compact metric space.Two subadditive variational principles associated with two different relatively weak conditions are developed for the defined topological pressure.As an application,we give an example on systems with nonzero Lyapunov exponents.     

A note on a theorem of Tacon

In this paper we give the minimal conditions which must satisfy families of subsets ofF for the proof of a theorem of Tacon and analogous results for some other classes of operatorsT:E→F defined via these families can be reproduced.     

Fell-拓扑的伪紧性（英文）

设X是拓扑空间，CL（X）表示X的所有非空闭子集的族，本文得到了下述结果：在CL（X）上的Fell-拓扑是伪肾的当且仅当X是feebly-紧或者非局部紧或者非σ－紧，由此得到了对于伪紧性不是闭遗传的两类新的拓扑空间。     

Connectedness and compactness on standard sets

We present a nonstandard characterization of connected compact sets (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

最强Orlicz-Pettis拓扑

引进了lp（p≥1）空间的子集是本性紧概念,借此给出了抽象对偶系统（E,F）中最强Orlicz－Petits拓扑SOP（E,F）以及产生该拓扑的最大映射集族的表示．利用此结果搞清楚了现有两种Orlicz－Petits拓扑即Dierolf拓扑（M）和Twed－dle拓扑（E,T’）的确切意义以及它们之间的相互关系．指出了的最大性所蕴涵的理论意义和应用价值．证实了σ（F,E）-条件紧集和σ（F,E）-可数紧集都含于中。进而实质性地改进了矢位测度论中的Graves－Rness定理、抽象函数论中的Thomas定理等重要结果．