算子子空间的渐近自反性和遗传性

研究了算子子空间的渐近自反性问题，渐近自反子空间的遗传斯近自反性以及某些单个算子的渐近自反性．我们也讨论了投影网类的浙近自反性。     

超自反的子空间格

本文讨论了子空间格的自反性和超自反性，给出了子空间格是超自反的等价条件．     

自反Banach空间上算子代数的超自反性

本文引入自发Banach空间上算子代数A的超自反定义，讨论了A超自反的充要条件，超自反常数的估计以及超自反在代数同构下的不变性。     

自反和超自反子空间格

本文讨论了子空间格的序和、序积的自反和超自反性以及它们对应的代数的超自反性。     

算子矩阵代数的自反性和超自反性

本文总假定 H 是可分的 Hilbert 空间;L(H)表示 H 上有界线性算子全体;而 L(?)(H)表示 L(H)上σ-ω算子拓扑连续的线性泛函全体.设(?)L(H)为σ-ω算子拓扑闭的子代数,(?)称为自反的是指(?)=Alg Lat(?)={T∈L(H):TE(?)E (?)E∈Lat(?)},其中 Lat(?)是(?)的不变子空间格.(?)称为超自反的是指存在常数 K>0,使对任意的 T∈L(H)有 d(T,(?))≤K sup{‖P_M~(?)TP_M‖∶M∈Lat(?)}.其中 P_M 是指到 M 上的自伴投影。有关算子代数的超自反性已有一些结果,例如见     

自反代数的双局部导子

证明了自反Banach空间X中自反代数A到B(x)的导子集合是拓扑代数双自反的.     

关于超自反算子代数

本文讨论了超自反算子代数的等价条件及超自反性在张量积、直和、同构、约化中的不变性，改进加深了孙善利＾［２］的结果，并证明了两类Ｖｏｎ Ｎｅｕｍａｎｎ代数的超自反性。     

包含广义亚自反空间的Banach空间

无穷维Banach空间理论中一个基本问题是:每一个Banach空间都包含一个子空间与c_0或l~1自反空间同构? M·valsivia[1]建立了如下结果。     

自反BCK－代数

本文在ＢＣＫ－代数中引进稳定子的概念，并定义一类特殊的ＢＣＫ－代数─自反ＢＣＫ－代数，证明自反ＢＣＫ－代数的概念与半单ＢＣＫ－代数的概念是一致的，同时对于有限ＢＣＫ－代数还得到它是自反的一个充要条件。     

关于非交换子空间格代数的超自反性

利用Ａｒｖｅｓｏｎ关于自反代数超自反的特征，给出Ｈｉｌｂｅｒｔ空间上一类非交换格自反代数超自反常数的一个估计，证明了一些非交换子空间格自反代数的超自反性．     

A Note on Reflexivity

We prove some new results on Hadwin's general version of reflexivity that reduce the study of E-reflexivity (or E-hyperreflexivity) of a linear subspace to a smaller linear subspace. By applying our abstract results, we present a simple proof of D. Hadwin's theorem, which states that every C^∗-algebra is approximately hyperreflexive. We also prove that the image of any C^∗-algebra under any bounded unital homomorphism into the operators on a Banach space is approximately reflexive. We introduce a new version of reflexivity, called approximate algebraic reflexivity, and study its properties.     

ON REFLEXIVITY OF HYPONORMAL AND WEIGHTED SHIFT OPERATORS

By an elementary proof, we use a result of Conway and Dudziak to show that if A is a hyponormal operator with spectral radius r(A) such that its spectrum is the closed disc {z:|z| ≤ r(A)} then A is reflexive. Using this result, we give a simple proof of a result of Bercovici, Foias, and Pearcy on reflexivity of shift operators. Also, it is shown that every power of an invertible bilateral weighted shift is reflexive.     

ON REFLEXIVITY AND HYPERREFLEXICITY FOR LINEAR SUBSPACE OF OPERATORS.

It is proved that any Von Neymann type subspace is feflexive. Partioularly, all weakly closed-algebras and their weakly closed ideals are reflexive. Some results concerning hyperreflexivity of Von Neumann type subspace and Von Neumand algebra are obtained.     

线性距离空间的一致凸性与自反性

本文研究了线性距离空间的一致凸性与自反性，同时对吴从Ｘｉｎ等提出的严格缩条件能否去掉的问题给出了肯定的答案。     

自反算子代数的模和交换子以及一阶上同调空间

设L是赋范线性空间上的子空间格,一个子空间是自反AlgL-模的充分必要条件被得到,当L是完全分配子空间格时,自反AlgL-模的二次交换子被描述,进而,本文引入V-生成子稠格,这是一种严格地包含了完全分配格和五角格的格类。当L是可换的V-生成子稠格时,模模交换子C(AlgL;M)和代数AlgLatM都被分解成直和,并且满足条件H~1(AlgL,B(H))=0的一阶上同调空间H~1(AlgL,M)被刻划。     

Many Familiar Categories can be Interpreted as Categories of Generalized Metric Spaces

The simple concepts of (general) distance function and homometry (a map that preserves distances up to a calibration) are introduced, and it is shown how some natural distance functions on various mathematical objects lead to concrete embeddings of the following categories into the resulting category DIST°: quasi-pseudo-metric, topological, and (quasi-)uniform spaces with various kinds of maps; groups and lattice-ordered abelian groups; rings and modules, particularly fields; sets with reflexive relations and relation-preserving maps (particularly directed loop-less graphs and quasi-ordered sets); measured spaces with Radon-continuous maps; Boolean, Brouwerian, and orthomodular lattices; categories with combined objects, for example topological groups, ordered topological spaces, ordered fields, Banach spaces with linear contractions or linear continuous maps and so on.     

Über einen Graphensatz für Abbildungen mit normiertem Zielraum

This paper contains a detailed study of those locally convex spaces E-which we call GN-spaces-for which the following closed graph theorem holds: Every closed linear map from E to any normed linear space is continuous. In the first two sections we establish some characterisations and permanence-properties of these spaces. The main result reads as follows: Every separated GN-space is isomorphic to a barrelled subspace of some ω_d?_d′, and conversely. Then we determine those GN-spaces which are (DF)-spaces, Schwartz-spaces or nuclear spaces. Finally we show that neither the strong dual nor the tensor product of GN-spaces are GN-spaces.     

关于纤维一般拓扑的一点注记(英文)

Some characterizations of paracompact maps are given in this note, and some equivalent statements of collectionwise normal maps are discussed. And also we show that if f ： X→Y is a closed collectionwise normal map, and f^-1（y） is a semistratifiable subspace of X for any y ∈ Y, then f is a paracompact map.     

Invariant manifolds of maps close to a product of rotations: close to the rotation axis

We consider families of maps depending on a parameter ε such that for ε=0 the map becomes a product of linear rotations in and for ε≠0 the map is weakly attracting in the product of the rotation planes and weakly repelling in some complementary subspace. We prove that the unstable manifold converges to the complementary subspace in the C^r topology, the case r=∞ included. We consider both the local and the global manifolds. For that we prove some results on families of maps near a norm one linear map, which are of independent interest.     

On closed subspaces with Schauder bases in non-archimedean Fréchet spaces

The main purpose of this paper is to prove that a non-archimedean Fréchet space of countable type is normable (respectively nuclear; reflexive; a Montel space) if and only if any its closed subspace with a Schauder basis is normable (respectively nuclear; reflexive; a Montel space). It is also shown that any Schauder basis in a non-normable non-archimedean Fréchet space has a block basic sequence whose closed linear span is nuclear. It follows that any non-normable non-archimedean Fréchet space contains an infinite-dimensional nuclear closed subspace with a Schauder basis. Moreover, it is proved that a non-archimedean Fréchet space E with a Schauder basis contains an infinite-dimensional complemented nuclear closed subspace with a Schauder basis if and only if any Schauder basis in E has a subsequence whose closed linear span is nuclear.