超积空间及其性质

引进了和内积空间没有相互包含关系的一类新空间:超积空间,进而研究了超积空间的性质.这类新的线性空间具有许多内积空间的重要性质,从而得到了线性空间一类新的度量刻画.     

序列位差空间的拓扑性质

利用拓扑学的一般理论,研究了序列位差空间的连通性,给出了序列位差空间为可分空间、紧致空间的充分必要条件.     

Stein domains in Banach algebraic geometry

In this article we give a homological characterization of the topology of Stein spaces over any valued base field. In particular, when working over the field of complex numbers, we obtain a characterization of the usual Euclidean (transcendental) topology of complex analytic spaces. For non-Archimedean base fields the topology we characterize coincides with the topology of the Berkovich analytic space associated to a non-Archimedean Stein algebra. Because the characterization we used is borrowed from a definition in derived geometry, this work should be read as a derived perspective on analytic geometry.     

Metrically generated theories

Many examples are known of natural functors describing the transition from categories of generalized metric spaces to the ``metrizable" objects in some given topological construct . If preserves initial morphisms and if is initially dense in , then we say that is -metrically generated. Our main theorem proves that is -metrically generated if and only if can be isomorphically described as a concretely coreflective subconstruct of a model category with objects sets structured by collections of generalized metrics in and natural morphisms. This theorem allows for a unifying treatment of many well-known and varied theories. Moreover, via suitable comparison functors, the various relationships between these theories are studied.

     

关于弱MCP空间与弱层空间

本文引入了与已知的一些空间类非常类似的两个概念,我们分别称它们为弱MCP空间与弱层空间.本文主要讨论了这两空间类的等价命题与一些基本性质,及它们与原有空间类的关系.     

鞅空间理论的新进展

本文是一篇综述性的文字,内容主要是近年来有关鞅空间理论的发展状况,特别是集中于B-值鞅和弱型鞅空间两个部分,可以看做是整个鞅空间理论发展的一个侧面.希望以此引起读者对鞅论的了解和进一步研究的兴趣.具体内容分为以下三节:1.研究鞅空间理论的意义,阐述鞅空间理论与调和分析的关系;2.鞅空间理论的向量值化,阐述B-值鞅不等式与Banach空间几何学的相互依存关系;3.弱型鞅空间与变指数鞅空间的不等式及其应用.     

De Branges-Rovnyak spaces and Dirichlet spaces

Sarason has shown that the local Dirichlet spaces Dλ may be considered as manifestations of de Branges-Rovnyak spaces H(b), and has used this identification to give a new proof that the spaces Dλ are star-shaped. We investigate which other Dirichlet spaces D(μ) arise as de Branges-Rovnyak spaces, and which other de Branges-Rovnyak spaces H(b) are star-shaped. We also prove a transfer principle which represents H(b)-spaces inside Dλ.     

关于k-半层空间的一些结果

给出了对k-半层空间及c-半层空间的一些等价刻画,并给出kβ空间成为k-半层空间的一些条件.     

k-super-strongly convex and k-super-strongly smooth Banach spaces

In this paper, we introduce two types of new Banach spaces: k-super-strongly convex spaces and k-super-strongly smooth spaces. It is proved that these two notions are dual. We also prove that the class of k-super-strongly convexifiable spaces is strictly between locally k-uniformly rotund spaces and k-strongly convex spaces, and obtain some necessary and sufficient conditions of k-super-strongly convex space (respectively k-super-strongly smooth space). Also, for each k?2, it is shown that there exists a k-super-strongly convex (respectively k-super-strongly smooth) space which is not (k−1)-super-strongly convex (respectively (k−1)-super-strongly smooth) space.     

A characterization of Bloch space and Besov space

On the unit disk of the complex plane, a characterization for the membership of Bloch space and analytic Besov space is expressed extending known results.     

Hyperbolic Hilbert space

The hyperbolic complex space is one class of non-Euclidean spaces with continuous singular points. It corresponds with Minkowski space, and it has the characteristic that the space-time direction is different in nature. Regard the hyperbolic complex space as original spaces. We can abstract a class of the hyperbolic inner product space and the hyperbolic Hilbert space.     

The Priestley Separation Axiom for Scattered Spaces

Let R be a quasi-order on a compact Hausdorff topological space X. We prove that if X is scattered, then R satisfies the Priestley separation axiom if and only if R is closed in the product space X×X. Furthermore, if X is not scattered, then we show that there is a quasi-order on X that is closed in X×X but does not satisfy the Priestley separation axiom. As a result, we obtain a new characterization of scattered compact Hausdorff spaces.     

核局部凸空间的一个新特征

Ａ．Ｐｉｅｔｓｃｈ＾［１］在讨论核局部凸空间时给出了两类矢值序列空间ｌ１［Ｘ］和ｌ１｛Ｘ｝。本文建立了矢值序列空间ｌ１［Ｘ］及ｌ１｛Ｘ｝和连续线性算子空间Ｌ（ｃ０，Ｘ）及绝对可和算子空间ＡＳ（ｃ０，Ｘ）之间的拓扑同胚关系。通过ｃ０上的矢值算子类Ｌ（ｃ０，Ｘ）和ＡＳ（ｃ０，Ｘ）及其上的拓扑等价关系，对局部凸空间Ｘ是核空间给出了一个新的特征刻划。     

Some open problems concerning q-convexity and Stein spaces

We discuss some open problems in the theory of analytic pseudoconvexity. We focus our attention especially on q-complete spaces and Stein spaces.     

The behaviour on the rays of functions from the Bergman and Fock spaces

In this note we study the behaviour of holomorphic functions from the Bergman and Fock spaces on the rays of the unit disc U and the complex plane ℂ. We obtain conditions on the finiteness of weighted L ²-integrals of those functions along rays.      

A generalization of Hardy spaces <Emphasis Type="Italic">H</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> by using atoms

Let X = （X, d,μ） The purpose of this paper is to be a space of homogeneous type in the sense of Coifman and Weiss. generalize the definition of Hardy space H^P（X） and prove that the generalized Hardy spaces have the same property as H^P（X）. Our definition includes a kind of Hardy- Orlicz spaces and a kind of Hardy spaces with variable exponent. The results are new even for the R^n case. Let （X, δ, μ） be the normalized space of （X, d, μ） in the sense of Macias and Segovia. We also study the relations of our function spaces for （X, d, μ） and （X, δ,μ）.     

B-值鞅Hardy空间与BMO空间的实内插

研究了B值鞅Hardy空间与BMO空间的实内插，并利用所得结果，讨论了鞅Hardy空间的内插空间的共轭问题。     

Multi Fuzzy Fractal Theorems in Fuzzy Metric Spaces

The Hutchinson-Barnsley (HB) operators are studied for multi iterated function system in a general setting. Some existence and uniqueness results are obtained in fuzzy fractal and multi fuzzy fractal spaces. From them, we obtain our results, which generalize some recent results in the literature.     

Finite and -resolvability

A topological space is -resolvable if has disjoint dense subsets. In this paper, we prove that if is -resolvable for each positive integer , then is -resolvable.