The strong approximation property

We introduce and investigate the strong approximation property of Banach spaces which is strictly stronger than the approximation property and at least formally weaker than the weak bounded approximation property. Among others, we show that the weak bounded approximation property is equivalent to a quantitative strengthening of the strong approximation property. Some recent results on the approximation property of Banach spaces and their dual spaces are improved.     

When does the Haver property imply selective screenability?

We point out that in metric spaces Haver's property is not equivalent to the property introduced by Addis and Gresham. We prove that they are equal when the space has the Hurewicz property. We prove several results about the preservation of Haver's property in products. We show that if a separable metric space has the Haver property, and the nth power has the Hurewicz property, then the nth power has the Addis-Gresham property. R. Pol showed earlier that this is not the case when the Hurewicz property is replaced by the weaker Menger property. We introduce new classes of weakly infinite dimensional spaces.     

Weak and quasi approximation properties in Banach spaces

In this paper, we introduce weak versions (the weak approximation property, the bounded weak approximation property, and the quasi approximation property) of the approximation property and derive various characterizations of these properties. And we show that if the dual of a Banach space X has the weak approximation property (respectively the bounded weak approximation property), then X itself has the weak approximation property (respectively the bounded weak approximation property). Also we observe that the bounded weak approximation property is closely related to the quasi approximation property.     

The Lyndon property and uniform interpolation over the Grzegorczyk logic

We consider versions of the interpolation property stronger than the Craig interpolation property and prove the Lyndon interpolation property for the Grzegorczyk logic and some of its extensions. We also establish the Lyndon interpolation property for most extensions of the intuitionistic logic with Craig interpolation property. For all modal logics over the Grzegorczyk logic as well as for all superintuitionistic logics, the uniform interpolation property is equivalent to Craig’s property.     

The positive-divergence and blowing-up properties

A property of ergodic finite-alphabet processes, called the blowing-up property, is shown to imply exponential rates of convergence for frequencies and entropy, which in turn imply a positive-divergence property. Furthermore, processes with the blowing-up property-divergence property. Furthermore, processes with the blowing-up property are finitely determined and the finitely determined property plus exponential rates of convergence for frequencies and for entropy implies blowing-up. It is also shown that finitary codings of i.i.d. processes have the blowing-up property. Partially supported by Hungarian National Foundation for Scientific Research Grant OTKA 1906. Partially supported by NSF grant DMS-9024240.     

算子空间中秩一算子的稠密性

设u是Hilbert空间上的σ-弱闭算子空间,称u具有性质（P）,如果u中秩－算子生成的子空间在u中是σ－弱稠密的,称u具有扩张性质（P）,如果u以及包含u的每个σ－弱闭子空间都具有性质（P）,本文研究了性质（P）和扩张性质（P）,给出了它们的等从描述。     

逐点伪轨跟踪性质及其应用

本文给出紧致度量空间逐点伪轨跟踪性质的定义,该定义是伪轨跟踪性质定义的推广.作为应用,证明如下结论:(i)若f具有逐点伪轨跟踪性质,且对任意k∈Z ,fk为链转换的,那么对任意k∈Z ,fk为开集转换;(ii)若f具有逐点伪轨跟踪性质,且对任意n∈Z ,fn为链转换的,则f具有初始敏感依赖性质;(iii)若f为开集混合的,且具有逐点伪轨跟踪性质,那么f具有性质P;(iv)设f:(X,d)→(X,d)是同胚映射,那么f具有逐点伪轨跟踪性质当且仅当移位映射σf具有逐点伪轨跟踪性质.     

Strong CHIP, normality, and linear regularity of convex sets

We extend the property (N) introduced by Jameson for closed convex cones to the normal property for a finite collection of convex sets in a Hilbert space. Variations of the normal property, such as the weak normal property and the uniform normal property, are also introduced. A dual form of the normal property is derived. When applied to closed convex cones, the dual normal property is the property (G) introduced by Jameson. Normality of convex sets provides a new perspective on the relationship between the strong conical hull intersection property (strong CHIP) and various regularity properties. In particular, we prove that the weak normal property is a dual characterization of the strong CHIP, and the uniform normal property is a characterization of the linear regularity. Moreover, the linear regularity is equivalent to the fact that the normality constant for feasible direction cones of the convex sets at is bounded away from 0 uniformly over all points in the intersection of these convex sets.

     

The Ideal Extension and Congruence Extension Properties for Compact Semigroups

The aim of this paper is to study the congruence extension property and the ideal extension property for compact semigroups. We present a characterization of compact semigroups with the ideal extension property and prove that each compact semigroup with the congruence extension property also has the ideal extension property.     

知识产权产品与经济发展水平关系研究——基于突变级数法和ARDL模型

知识产权产品是一个全新的概念,SNA2008将用于国民经济核算的"无形固定资产"重新定义为"知识产权产品",这种修改凸显了知识产权产品在评价国民经济发展中的重要作用。本文收集了1995-2013年多个与我国知识产权产品与经济发展水平相关的数据,使用突变级数法建立知识产权产品和经济发展水平两个指标体系,以此计算两者的综合评价得分,然后运用ARDL模型对两者进行协整检验。检验结果表明,知识产权产品和经济发展水平之间在长期内存在显著的相互影响。     

Property of Kelley for confluent retractable continua

The property of Kelley for confluent retractable continua is studied. It is shown that a confluent retractable continuum has the property of Kelley if and only if each of its proper subcontinua has the property. An example is constructed of a confluent retractable continuum without the property of Kelley.     

Kadec-Klee property in Musielak-Orlicz function spaces equipped with the Orlicz norm

It is well-known that the Kadec-Klee property is an important property in the geometry of Banach spaces. It is closely connected with the approximation compactness and fixed point property of non-expansive mappings. In this paper, a criterion for Musielak-Orlicz function spaces equipped with the Orlicz norm to have the Kadec-Klee property are given. As a corollary, we obtain that a class of non-reflexive Musielak-Orlicz function spaces have the Fixed Point property.

     

Some Weak Specification Properties and Strongly Mixing

In this paper,the authors first construct a dynamical system which is strongly mixing but has no weak specification property.Then the authors introduce two new concepts which are called the quasi-weak specification property and the semi-weak specification property in this paper,respectively,and the authors prove the equivalence of quasi-weak specification property,semi-weak specification property and strongly mixing.     

Banach空间的p-弱近似性质

给出了Banach空间的p-弱近似性质和p-有界弱近似性质的定义,获得了这些性质的一些刻画.利用这些刻画证明了如果一个Banach空间X的对偶空间X~*有p-弱近似性质(或p-有界弱近似性质),则X有p-弱近似性质(或p-有界弱近似性质),在一般情况下反之不成立.     

第n根性质与根环

令E为 (MR)的自同态环 ,本文首先证明了MR 有第n根性质的充要条件是EE 有第n根性质 ,由此引进了根环的概念 ,并研究了根环的性质。特别地我们证明了如nA nB且A拟内射 ,则A B .     

Detecting codimension one manifold factors with 0-stitched disks

The 0-stitched disks property is introduced and shown to detect codimension one manifold factors of dimension n?4. It is shown that if a space X is an ANR and has the 0-stitched disks property, then X has the disjoint homotopies property. It follows that if a space X is a resolvable generalized manifold of dimension n?4 with the 0-stitched disks property, then X is a codimension one manifold factor. Whether or not the 0-stitched disks property is equivalent to the disjoint homotopies property remains an open question.     

Dual problems for weak and quasi approximation properties

It is shown that for the separable dual X^∗ of a Banach space X if X^∗ has the weak approximation property, then X has the metric quasi approximation property. Using this it is shown that for the separable dual X^∗ of a Banach space X the quasi approximation property and metric quasi approximation property are inherited from X^∗ to X and for a separable and reflexive Banach space X, X having the weak approximation property, bounded weak approximation property, quasi approximation property, metric weak approximation property, and metric quasi approximation property are equivalent. Also it is shown that the weak approximation property, bounded weak approximation property, and quasi approximation property are not inherited from a Banach space X to X^∗.     

The weak metric approximation property

We introduce and investigate the weak metric approximation property of Banach spaces which is strictly stronger than the approximation property and at least formally weaker than the metric approximation property. Among others, we show that if a Banach space has the approximation property and is 1-complemented in its bidual, then it has the weak metric approximation property. We also study the lifting of the weak metric approximation property from Banach spaces to their dual spaces. This enables us, in particular, to show that the subspace of c₀, constructed by Johnson and Schechtman, does not have the weak metric approximation property. The research of the second-named author was partially supported by Estonian Science Foundation Grant 5704 and the Norwegian Academy of Science and Letters.     

拓扑线性空间中的Drop定理与Drop性质

给出了拓扑线性空间中的一个Drop定理.利用此Drop定理,证明了拓扑线性空间中的每个序列紧凸集具有Drop性质;每个可数紧闭凸集具有拟Drop性质.而且结出了拓扑线性空间中Drop性质和拟Drop性质的序列流特征.也讨论了Drop性质和拟Drop性质与泛函取极值之间的联系.     

Geometric exchange properties in lattices of finite length

We investigate geometric exchange properties in lattices of finite length that generalize the Steinitz exchange property of finite-dimensional vector spaces. In particular, we show that a stronger version of MacLane's exchange property for semimodular lattices is equivalent to the join-symmetric exchange property of Gaskill and Rival for modular lattices and, furthermore, that this exchange property characterizes strong semimodular lattices. An analogue of the basis exchange property for matroids is considered and seen to distinguish strong lattices in the class of semimodular lattices.Presented by I. Rival.