关于Banach空间的遗传不能分解和商遗传不能合成性质

该文说明遗传不能分解空间上的黎斯算子类构成了最大、非平凡的算子理想，简化了Gowers和Maurey关于这类空间上算子构成的推证．应用对偶原理，引入商遗传不能合成的概念，讨论商遗传不能合成的Banach空间上的算子构成，得到了相应的一些结果．     

关于G-M成果研究的若干新动态Ⅱ--与G-M型空间相关的算子

结合自己的工作，对Gowers-Maurey系列成果获Fields奖以来的研究的新动态作一综述，该是下篇，主要讨论与G-M型空间相关的算子，包括可通过G-M型空间分解的算子，G-M型空间上的算子理想与算子构成，G-M型空间上的算子谱理论等。     

某些G-M型Banach空间及其上算子代数的Κ-群

按分解与合成性质给出G-M型Banach空间的若干新品种,讨论这些空间上的算子构成;通过对含于Riesz算子类的算子理想的K-群的计算,讨论这些G-M型Banach空间上算子代数的K-理论。     

某些G-M型Banach空间及其上算子代数的K-群

按分解与合成性质给出G-M型Banach空间的若干新品种, 讨论这些空间上的算子构成; 通过对含于Riesz算子类的算子理想的K-群的计算, 讨论这些G-M型Banach空间上算子代数的K-理论.     

超sober空间的若干基本性质

本文主要讨论超sober空间的一些基本性质，对三类特殊空间的超sober性进行了讨论，并对T₀空间X的超sober性与其Smyth幂空间、Hoare幂空间的超sober性之间的关系进行了讨论；用反例说明了可数无限多个超sober空间的乘积一般不是超sober的；证明了若T₀空间X不是超sober的，则其超sober化不存在。     

定向闭包空间的若干性质

拓扑空间X称为定向闭包空间(简称DC空间),若它是T₀的，且其任一既约闭集都是某定向子集的闭包，此处X赋予特殊化序。本文讨论了定向闭包空间的一些基本性质，证明了偏序集赋予Alexandroof拓扑所得空间和其Smyth幂空间都是DC空间；偏序集赋予上拓扑是quasisober空间当且仅当它是DC空间；DC性对开子空间遗传，但对饱和子空间一般不遗传；对T₀空间X,其Smyth幂空间是DC空间一般不蕴含X是DC空间。     

Banach空间的无穷维子空间结构的若干问题

本文论述了关于Ｂａｎａｃｈ空间的无穷维子空间结构的两分枝问题，三分枝问题和无条件基序列的存在性等五个问题，这些是当前Ｂａｎａｃｈ空间理论中尚未解决的几个基本问题，同时介绍了试图解决这几个问题的有关概念和方法如Ｂａｎａｃｈ空间的稳定性，扭曲范数和空间的饱合性等。     

关于GB型空间的若干结果

本文对GB型空间进行了若干讨论,得到了一些结果。 设X为Banach空间,X为X的共轭空间,B(X,X)为X到X的所有有界线性算子组成的空间。如果X中的弱收敛序列为弱收敛序列,则称X为GB型空间。Grothendieck.A于1953年证明了l~∞是GB型空间。显然自反空间是GB型空间。     

关于S（n）—θ—闭空间

Ｄｉｋｒａｎｊａｎ与Ｇｉｕｌｉ引入了θ＾ｎ－闭包算子，定义了Ｓ（ｎ），Ｓ（ｎ）－闭和Ｓ（ｎ）－θ－闭空间，建立了Ｓ（ｎ）－θ－闭空间理论，并提出了６个公开问题，本文将从Ｓ（ｎ）－θ－空间的极小性和乘积性来介绍Ｓ（ｎ）－θ－闭空间理论的最新进展，文中的三个拓扑反例否定回答了Ｄｉｋｒａｎｊａｎ与Ｇｉｕｌｉ提出的４个公开问题。     

具有σ遗传闭包保持双网的空间

证明了正则空间X具有σ遗传闭包保持双网当且仅当或X是cosmic空间，或X是σ闭离散空间，回答了[1]提出的一个问题．     

Inverse limits of hereditarily almost expandable class

In this paper, the hereditarily almost expandability of inverse limits is investigated, with two results obtained. Let X be the inverse limit space of an inverse system （Xα, π^αβ, ∧}. （1） Suppose X is hereditarily κ-metacompact, if each Xα is hereditarily pointwise collectionwise normal （almost θ-expandable, almost discrete θ-expandable）, then so is X; （2） Suppose X is hereditarily κ-σ-metacompact, if each Xα is hereditarily almost σ-expandable （almost discrete σ-expandable = σ-pointwise collectionwise normal）, then so is X.     

The product of a Baire space with a hereditarily Baire metric space is Baire

In this paper we prove that the product of a Baire space with a metrizable hereditarily Baire space is again a Baire space. This answers a recent question of J. Chaber and R. Pol.

     

Some G-M-type Banach spaces and K-groups of operator algebras on them

By providing several new varieties of G-M-type Banach spaces according todecomposable and compoundable properties, this paper discusses the operator structuresof these spaces and the K-theory of the algebra of the operators on these G-M-type Ba-nach spaces through calculation of the K-groups of the operator ideals contained in theclass of Riesz operators.     

A small Dowker space in ZFC

We construct a hereditarily normal topological space whose product with the unit interval is not normal. The space is -relatively discrete and has cardinality of the continuum .

     

Stability Characterizations of ε-isometries on Certain Banach Spaces

Suppose that X, Y are two real Banach Spaces. We know that for a standard ε-isometry f : X → Y, the weak stability formula holds and by applying the formula we can induce a closed subspace N of *. In this paper, by using again the weak stability formula, we further show a sufficient and necessary condition for a standard ε-isometry to be stable in assuming that N is w*-closed in Y*.Making use of this result, we improve several known results including Figiel's theorem in reflexive spaces.We also prove that if, in addition, the space Y is quasi-reflexive and hereditarily indecomposable, then L(f)≡span[f(X)] contains a complemented linear isometric copy of X; Moreover, if X =Y, then for every e-isometry f: X → X, there exists a surjective linear isometry S:X → X such that f-S is uniformly bounded by 2ε on X.     

On Hereditarily Indecomposable Banach Spaces

This paper shows that every non-separable hereditarily indecomposable Banach space admits an equivalent strictly convex norm, but its bi-dual can never have such a one; consequently, every non-separable hereditarily indecomposable Banach space has no equivalent locally uniformly convex norm.     

On the existence of chaotic and hypercyclic semigroups on Banach spaces

We prove that every separable infinite dimensional complex Banach space admits a hypercyclic uniformly continuous semigroup. We also prove that there exist Banach spaces admitting no chaotic strongly continuous semigroups.

     

Some Characterizations of Hereditarily Indecomposable Banach Spaces

In this paper we first discuss the relations between some G-M-type spaces, and the previous eight kinds of G-M-type Banach spaces are merged into four different kinds. Then we build a Generalized Operator Extension Theorem, and introduce the concept of complete minimal sequences. Some sufficient and necessary conditions under which a Banach space is a hereditarily indecomposable space are given. Finally, we give some characterizations of hereditarily indecomposable Banach Spaces.     

Hereditarily covering properties of inverse sequence limits

Let {X _i , π _k ⁱ , ω} be an inverse sequence and $X = \mathop {\lim }\limits_ \leftarrow \left\{ {X_i ,\pi _k^i ,\omega } \right\}$ . If each X _i is hereditarily (resp. metaLindelöf, σ-metaLindelöf, σ-orthocompact, weakly suborthocompact, δθ-refinable, weakly θ-refinable, weakly δθ-refinable), then so is X.