具有S-WGHP性质的对偶对

In this paper,we introduce the signed weak gliding hump property in a dual pair with the sturcture of a system of sections and show that if a dual pair [E,F] has the signed weak gliding hump property,then the β-dual space of E is a weak sequentially complete space if and only if for every n ∈N,(F^[n],σ(F^[n],E^[n]))is sequentially complete,Furthermore,we also prove that if [E,F] has the signed weak gliding hump property,then (E,τ(E,F^（β）)is an AK-space.     

Remarks on B（D,λ）-refinability

In this paper, some equivalent versions of B(D,λ)-refinability are given. One of these equivalent versions, is that a space X is B(D, ωo)-refinable if and only if X is strongly quasi-paracompact. As an application of the above result, the author shows that weak θ-refinability is strictly weaker than strong quasi-paracompactness in T4-spaces, which answers a question posed by Jiang. In addition, the author proves that a weak version of B(D,λ) always implies weak θ-refinability for any λ<ω1, and also give a T4, B(D,ωo)-refinable (=strongly quasi-paracompact) space which is not θ-refinable.     

THE FUNCTIONAL DIMENSION OF SOME CLASSES OF SPACES

The functional dimension of countable Hilbert spaces has been discussed by some authors. They showed that every countable Hilbert space with finite functional dimension is nuclear. In this paper the authors do further research on the functional dimension, and obtain the following results: (1) They construct a countable Hilbert space, which is nuclear, but its functional dimension is infinite. (2) The functional dimension of a Banach space is finite if and only if this space is finite dimensional. (3) Let B be a Banach space, B* be its dual, and denote the weak * topology of B* by σ(B*,B). Then the functional dimension of (B*,σ(B*,B)) is 1. By the third result, a class of topological linear spaces with finite functional dimension is presented.     

Parametrized Area Integrals on Hardy Spaces and Weak Hardy Spaces

In this paper, the authors prove that if Ω satisfies a class of the integral Dini condition, then the parametrized area integral μΩ,S^ρ is a bounded operator from the Hardy space H1 （R^n） to L1 （R^n） and from the weak Hardy space H^1,∞ （R^n） to L^1,∞ （R^n）, respectively. As corollaries of the above results, it is shown that μΩ,S^ρ is also an operator of weak type These conclusions are substantial improvement and （1, 1） and of type （p,p） for 1 〈 p 〈 2, respectively extension of some known results.     

Weakly Sequential Completeness of Orlicz Spaces

Banach space X is called to be weakly sequential complete space, if foreach weak Cauchy Sequence {x_n} in X, there exists a element in X such that x_n→x (n→∞). Weakly sequential completeness in close relationship with refrexivity、separability、weak convexity、bases and isomorphic subspaces in Banach spaces.     

RANDERS SPACES WITH SCALAR FLAG CURVATURE

Let(M, F) be an n-dimensional Randers space with scalar flag curvature. In this paper, we will introduce the definition of a weak Einstein manifold. We can prove that if(M, F) is a weak Einstein manifold, then the flag curvature is constant.     

Cc （X） Spaces with X Locally Compact

In this paper, we show, among other results, that if X is a [separable] locally compact space X [satisfying the first countability axiom] then the space Cc （X） has countable tightness [if and only if it has bounding tightness] if and only if it is Frechet-Urysohn, if and only if Cc （X） contains a dense （LM） subspace and if and only if X is a-compact.     

Toeplitz算子在Dirichlet空间上的亚正规性

In this paper,we prove that the necessary and sufficient condition for a Toeplitz operator Tu on the Dirichlet space to be hyponormal is that the symbol u is constant for the case that the projection of u in the Dirichlet space is a polynomial and for the case that u is a class of special symbols,respectively.We also prove that a Toeplitz operator with harmonic polynomial symbol on the harmonic Dirichlet space is hyponormal if and only if its symbol is constant.     

The Dissipative Quasi-geostrophic Equation in Weak Morrey Spaces

The author studies the Cauchy problem of the dissipative quasi-geostrophic equation in weak Morrey spaces. The global well-posedness is established for any small initial data in the weak space Mp^＊,γ（R^n）, with 1〈p〈∞and A = n-（2α-1）p, and for a small external force in a time-weighted weak Morrey space.     

ON CONDITIONS FOR THE NON LOCALLY CONVEX LINEAR TOPOLOGICAL SPACE TO HAVE THE H.-B. EXTENSION PROPERTY

In this paper, the conditions for the non lcally convex topological vector space to have the H,-B. extension property is discussed, and the following three results are proved; (1)A closed subspace E0 of a linear topological space E to have the H.-B. property if and only if for every closed hyperplane of E0 is weakly closed, (2) A locally bounded linear topological space (E,τo)to have the H.-B extension property if and only if for every closed subspace E0 of E, the weak topology σ(E0,E^*0)属于τ1|E0, where τ1 is the finest locally convex topology on E which is coarser then τ0. (3)Let E be separated and let E be the completion of E. If every closed subspace E0 of E is the complete hull of E0∩E,then E has H.-B. extension property if and only if E has H.-B. extension property.     

完全分配格代数中秩一子代数的弱稠密性和套代数的一个特征

如果　Ａ是　Ｈｉｌｂｅｒｔ　空间上的完全分配格代数，　　那么Ａ中秩一算子生成的子代数在　Ａ中弱稠密，　当且仅当，Ａ在迹尖算子空间中的一次和二次预零化子的弱闭包是自反的；如果Ａ是套代数，那么ＬａｔＡ是极大套，当且仅当，Ａ的包含Ａ－的每个弱闭子空间是自反的，其中     

Symmetrizable spaces and factor mappings

Main results: A pseudostratifiable symmetrizable space possesses a symmetric with weak Cauchy condition. A space is strongly symmetrizable if and only if it is a pseudo-open II-image of a metric space. There exists a zero-dimensional symmetrizable space without a symmetric with weak Cauchy condition.All spaces satisfy the axiom T₁.Translated from Matematicheskie Zametki, Vol. 14, No. 5, pp. 713–722, November, 1973.     

度量空间的序列复盖SS一映射

证明了如下结果：（l）拓扑空间X具有局评可数弱基当且仅当X＃A星空间的1一序列复盖商ss-掩映象；（2）拓升空间X具有局都可数基当且仅当XRk量空间的2一序列复盖商ss一映象．     

A note on complex spaces

For a family of closed balls in a normed space we define the concept of weak intersection property, and we show that a complex Banch space is a space if and only if every family of closed balls with the weak intersection property has a non-empty intersection.     

Very Convex Banach Spaces

ＶｅｒｙＣｏｎｖｅｘＢａｎａｃｈＳｐａｃｅｓＴｅｇｕｓｉ（特古斯）Ｓｕｙａｌａｔｕ（苏雅拉图）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＩｎｎｅｒＭｏｎｇｏｌｉａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｈｕｈｈｏｔ，０１００２２）ＬｉＹｏｎｇｊｉｎ...     

On interior regularity criteria for weak solutions of the navier-stokes equations

We are concerned with the behavior of weak solutions of the Navier-Stokes equations near possible singularities. We shall show that if a weak solution is in some Lebesgue space or small in some Lorentz space locally, it does not blowup there. Our basic idea is to estimate integral formulas for vorticity which satisfies parabolic equations.     

关于序列覆盖s映射

本文定义了两类序列覆盖映射，讨论了度晴空间的序列覆盖ｓ映象，特别地，我们证明了空间Ｘ具有点可数弱当且仅当Ｘ是度量空间的１序列覆盖的商ｓ映象，这回答了１９７０年Ｔ．Ｈｏｓｈｉｎａ提出了一个问题。     

广义函数Denjoy积分的收敛性问题

本文讨论广义函数De njoy积分的收敛性问题.首先给出了广义Denjoy可积函数空间中强收敛、弱收敛、弱~*收敛和广义函数Denjoy积分收敛的关系;证明拟一致收敛是广义函数Denjoy积分收敛的一个充分必要条件;最后指出了Denjoy可积广义函数列弱~*收敛与强收敛等价当且仅当原函数等度连续.     

When is a Volterra space Baire?

In this paper, we study the problem when a Volterra space is Baire. It is shown that every stratifiable Volterra space is Baire. This answers affirmatively a question of Gruenhage and Lutzer in [G. Gruenhage, D. Lutzer, Baire and Volterra spaces, Proc. Amer. Math. Soc. 128 (2000) 3115-3124]. Further, it is established that a locally convex topological vector space is Volterra if and only if it is Baire; and the weak topology of a topological vector space fails to be Baire if the dual of the space contains an infinite linearly independent pointwise bounded subset.     

The weak metric approximation property and ideals of operators

We study the weak metric approximation property introduced by Lima and Oja. We show that a Banach space X has the weak metric approximation property if and only if F(Y,X), the space of finite rank operators, is an ideal in W(Y,X∗∗), the space of weakly compact operators for all Banach spaces Y.