关于Lasnev空间的超空间

讨论了Ｌａｓｎｅｖ空间的超空间的某些性质．文中构造一反例，证明存在可数Ｌａｓｎｅｖ空间，其紧子集超空间不是层型空间．并指出文［６］中关于上述结果的证明中有一关键性失误，故［６］中的反例尚不能说明上述结论成立．本文还对具有σ－ＣＦ拟基的ｋ′空间给出一个刻画定理     

线性空间的亚子空间

本给出了线性空间中重子空间的概念，讨论了亚子空间的性质和维数，并将其应用到有解的非齐次线性方程组中去。     

线性空间的亚子空间

本文给出了线性空间中亚子空间的概念，讨论了亚子空间的性质和维数，并将其应用到有解的非齐次线性方程组中去．     

关于强J-空间与JHB-空间

引入了两个很有联系的空间类JHB-空间与强J HB-空间，分别推广了J-空间与强J-空间.讨论了J-空间、强J-空间、J HB-空间及强JHB-空间类间的相包含关系及此四空间类逆包含的条件，还得到了JHB-空间的内部刻画，并证明了若对每个α∈S，Xα.都是非紧的连通空间，则积空间∏α∈S Xα是强J-空间。     

内积空间的特征

本文在赋范线性空间中引进了一族角的概念，证明了这样定义的角中任一个满足某种几何性质，空间一定是内积空间。进而考虑相关正交性的概念和获得了内积空间的特征。     

关于S—Lindeloef空间及其子空间

本文是在半开集理论中提出了S－Lindeloef空间的概念。指S－Lindeloef空间是S－紧空间的一种推广，并对该空间及其子空间所具有的性质进行了一些有益的讨论。     

由给定的子空间构造新的子空间

本给出并证明了若干个子空间的并以及两个子空间的基构成子空间的充要条件，从而本质地揭示了除子空间的交与和是构造新的予空间的方法外，集合的其它运算不能构造新的子空间，最后分析了子空间直和的两种不同定义的优缺点，指出了张禾瑞教材中子空间直和定义推广时应注意的一个问题。     

模糊桶空间

文中给出了模糊桶空间的定义，在此基础上，研究了模糊桶空间的一系列重要定理。     

内积空间三角学与内积空间特征

本文建立了内积空间三角学，并对线性赋范空间给出了使它成为内积空间的三个新的充要条件。     

诱导空间的等价刻化及其应用

本文给出了诱导空间的几个等价的层次刻化，改进了已有的诱导空间中闭包（内部）算子层次刻化的结果，作为应用，我们推广了文「１」中有关分离性的几个定理。     

SOME RESULTS ABOUT BEST COAPPROXIMATION IN L^P（S,X）

As a counterpart to best approximation in normed linear spaces, the best coapproximation was introduced by Franchetti and Furi. In this paper, we shall consider the relation between coproximinality M in X and L ^p (S,M) in L ^p (S,X). Finally we give some results in cochebyshev subspaces and additional subspaces.     

Some remarks on quasi-Chebyshev subspaces

We give simple proofs of some results of Mohebi [H. Mohebi, On quasi-Chebyshev subspaces of Banach spaces, J. Approx. Theory 107 (2000) 87-95] on quasi-Chebyshev subspaces.     

On sum and quotient of quasi-Chebyshev subspaces in Banach spaces

It will be determined under what conditions types of proximinality are transmitted to and from quotient spaces.In the final section,by many examples we show that types of proximinality of subspaces in Banach spaces can not be preserved by equivalent norms.     

多圆盘的加权Bergman空间上的不变子空间和约化子空间

本文主要研究多圆盘的加权Bergman 空间上的不变子空间和约化子空间, 给出了某些解析Toeplitz 算子的极小约化子空间的完全刻画, 以及一类解析Toeplitz 算子Tzi (1≤i≤n) 的不变子空间的Beurling 型定理.     

A priori error bounds on invariant subspace approximations by block Krylov subspaces

We derive a priori error bounds for the block Krylov subspace methods in terms of “the sine” between the desired invariant subspace and the block Krylov subspace. The obtained results can be seen as the block analogue of the classical a priori estimates for standard projection methods.     

Wandering subspaces and quasi-wandering subspaces in the Hardy–Sobolev spaces

In this paper, we prove that for-1/2 ≤β≤0.suppose M is an invariant subspaces of the Hardy Sobolev spaces H_β~2(D) for T_z~β, then M() zM is a generating wandering subspace of M, that is,M=[MzM]_T_z~β Moreover, any non-trivial invariant subspace M of H_β~2(D) is also generated by the quasi-wandering subspace P_MT_z~βM~⊥ that is,M=[P_MT_z~βM~⊥]_(T_z~β).     

Completely distributive CSL algebras with no complements in

Anoussis and Katsoulis have obtained a criterion for the space to have a closed complement in , where is a completely distributive commutative subspace lattice. They show that, for a given , the set of for which this complement exists forms an interval whose endpoints are harmonic conjugates. Also, they establish the existence of a lattice for which has no complement for any . However, they give no specific example. In this note an elementary demonstration of a simple example of this phenomenon is given. From this it follows that for a wide range of lattices , fails to have a complement for any .