1.

Threespace problems for the bounded compact approximation property





Dong Yang Chen Ben Tuo Zheng《数学学报(英文版)》,2013年第29卷第4期


In this paper, the notion of the bounded compact approximation property (BCAP) of a pair [Banach space and its subspace] is used to prove that if X is a closed subspace of L∞ with the BCAP, then L∞/X has the BCAP. We also show that X* has the λBCAP with conjugate operators if and only if the pair (X, Y) has the λBCAP for each finite codimensional subspace Y∈X. Let M be a closed subspace of X such that M⊥ is complemented in X*. If X has the (bounded) approximation property of order p, then M has the (bounded) approximation property of order p.

2.

关于纤维一般拓扑的一点注记(英文)





彭良雪《东北数学》,2008年第24卷第4期


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.

3.

εWEAKLY CHEBYSHEV SUBSPACES OF BANACH SPACES





Sh.Rezapour《分析论及其应用》,2003年第19卷第2期


We will define and characterize cweakly Chebyshev subspaces of Banach spaces. We will prove that all closed subspaces of a Banach space X are εweakly Chebyshev if and only if X is reflexive.

4.

A Theorem for Generalized Extension of Operators and Some Applications





钟怀杰《东北数学》,2001年第17卷第4期


In this note it is shown that every bounded linear operator T Э B(Y，Z)defined on a closed subspace Y of a Banach space X admits a generalized extension T Э B(X, V). Some examples of the applications are given; especially, a characterization of H.I. spaces is obtained.

5.

Stability Characterizations of εisometries on Certain Banach Spaces





Li Xin Cheng Long Fa Sun《数学学报(英文版)》,2019年第35卷第1期


Suppose that X, Y are two real Banach Spaces. We know that for a standard εisometry 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 εisometry 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 quasireflexive and hereditarily indecomposable, then L(f)≡span[f(X)] contains a complemented linear isometric copy of X; Moreover, if X =Y, then for every eisometry f: X → X, there exists a surjective linear isometry S:X → X such that fS is uniformly bounded by 2ε on X.

6.

BEST APPROXIMATION BY DOWNWARD SETS WITH APPLICATIONS





H. Mohebi A. M. Rubinov《分析论及其应用》,2006年第22卷第1期


We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X

7.

Ballcovering property of Banach spaces that is not preserved under linear isomorphisms





Cheng LiXin Cheng QingJin and Liu XiaoYan《中国科学A辑(英文版)》,2008年第51卷第1期


By a ballcovering B of a Banach space X, we mean that it is a collection of open balls off the origin whose union contains the sphere of the unit ball of X. The space X is said to have a ballcovering property, if it admits a ballcovering consisting of countably many balls. This paper, by constructing the equivalent norms on l~∞, shows that ballcovering property is not invariant under isomorphic mappings, though it is preserved under such mappings if X is a Gateaux differentiability space; presents that this property of X is not heritable by its closed subspaces; and the property is also not preserved under quotient mappings.

8.

εPSEUDO CHEBYSHEV AND ε QUASI CHEBYSHEV SUBSPACES OF BANACH SPACES





Sh.Rezapour《分析论及其应用》,2004年第20卷第4期


We will define and characterize εpseudo Chebyshev and εquasi Chebyshev subspaces of Banach spaces. We will prove that a closed subspace W is εpseudo Chebyshev if and only if W is εquasi Chebyshev.

9.

The representations of generalized inverses of lower triangular operators





Chun Fang Shao Hong Ke Du Shu Feng Ji Jun Lian Xu《数学学报(英文版)》,2009年第25卷第12期


In this note, the explicit representations of MoorePenrose inverses of lower triangular operator matrices are established. As an application, the explicit representations of BottDuffin inverses of bounded linear operators on a Hilbert space with respect to a closed subspace are obtained.

10.

Second Order Nonlinear Evolution Inclusions Ⅰ： Existence and Relaxation Results





Nikolaos S. PAPAGEORGIOU Nikolaos YANNAKAKIS《数学学报(英文版)》,2005年第21卷第5期


This is the first part of a work on second order nonlinear, nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces and with a multivalued nonlinearity depending on both x（t） and x（t）. In this first part we prove existence and relaxation theorems. We consider the case of an usc, convex valued nonlinearity and we show that for this problem the solution set is nonempty and compact in C^1 （T, H）. Also we examine the Isc, nonconvex case and again we prove the existence of solutions. In addition we establish the existence of extremal solutions and by strengthening our hypotheses, we show that the extremal solutions are dense in C^1 （T, H） to the solutions of the original convex problem （strong relaxation）. An example of a nonlinear hyperbolic optimal control problem is also discussed.

11.

Schroedinger Flows on Compact Hermitian Symmetric Spaces and Related Problems





WeiYueDING HongYuWANG YouDeWANG《数学学报(英文版)》,2003年第19卷第2期


In this note,we prove that the Schroedinger flow of maps from a closed riemann surface into a compact irreducible Hermitian symmetic space admits a global weak solution.Also,we show the existence of weak solutions to the initial value problem of Heisenberg model with Lie algebra values,which is closely related to the Schroedinger flow on compact Hermitian symmetric spaces.

12.

METRIC ENTROPY OF HOMEOMORPHISM ON NONCOMPACT METRIC SPACE





周云华《数学物理学报(B辑英文版)》,2011年第31卷第1期


Let T : X → X be a uniformly continuous homeomorphism on a noncompact metric space (X, d). Denote by X* = X ∪ {x*} the one point compactification of X and T * : X* → X* the homeomorphism on X* satisfying T *X = T and T *x* = x*. We show that their topological entropies satisfy hd(T, X) ≥ h(T *, X*) if X is locally compact. We also give a note on Katok’s measure theoretic entropy on a compact metric space.

13.

取值于序拓扑向量空间的映射与层空间





杨二光 许云《数学研究及应用》,2018年第38卷第1期


In the paper [Monotone countable paracompactness and maps to ordered topological vector spaces, Top. Appl., 2014, 169(3): 51–70], Yamazaki initiated the study on maps with values into ordered topological vector spaces. Characterizations of monotonically countably paracompact spaces and some other spaces in terms of maps to ordered topological vector spaces were obtained. In this paper, following Yamazaki's method, we present some characterizations of stratifiable spaces and ksemistratifiable spaces in terms of maps with values into ordered topological vector spaces.

14.

ON LKUR SPACES 被引次数：1





俞鑫泰《数学年刊B辑(英文版)》,1985年第4期


In this paper it is proved that if X is an LKUR space,then X has(H)property andif X is an LKUR space,then X has RNP.Also,if M is a Chebyshev subspace of LKURspace,then P(M) is continuous.

15.

ON BEST SIMULTANEOUS APPROXIMATION IN QUOTIENT SPACES 被引次数：1





M. Iranmanesh H. Mohebi《分析论及其应用》,2007年第23卷第1期


We assume that X is a normed linear space, W and M are subspaces of X. We develop a theory of best simultaneous approximation in quotient spaces and introduce equivalent assertions between the subspaces W and W ＋ M and the quotient space W/M.

16.

CLOSED SMOOTH SURFACE DEFINED FROM CUBIC TRIANGULAR SPLINES





RenzhongFeng RenhongWang《计算数学(英文版)》,2005年第23卷第1期


In order to construct closed surfaces with continuous unit normal, we introduce a news pline space on an arbitrary closed mesh of threesided faces. Our approach generalizes an idea of Goodman and is based on the concept of ‘Geometric continuity‘ for piecewise polynomial parametrizations. The functions in the spline space restricted to the faces are cubic triangular polynomials. A basis of the spline space is constructed of positive functions which sum to 1. It is also shown that the space is suitable for interpolating data at the midpoints of the faces。

17.

Weakly Sequential Completeness of Orlicz Spaces





王玉文《数学研究与评论》,1986年第1期


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.

18.

On Gliding Hump Properties of Matrix Domains





Zheng Fu Tao Yuanhong Li Ronglu《东北数学》,2009年第25卷第1期


In this note, we establish several results concerning the gliding hump properties of matrix domains. In order to discuss FWGHP, we introduce the UAKproperty and find that this sort of property has close relationship with FWGHP. In the course of discussing FWGHP and WGHP of （C0）cn, we discuss the FWGHP and WGHP of the almostnull sequence space f0.

19.

CHARACTERIZATION OF BEST APPROXIMATIONS IN METRIC LINEAR SPACES





SizweMabizela《分析论及其应用》,2003年第19卷第2期


Let (X,d) be a real metric linear space, with translationinvariant metric d and G a linear subspace of X. In this paper we use functionals in the Lipschitz dual of X to characterize those elements of G which are best approximations to elements of X. We also give simultaneous characterization of elements of best approximation and also consider elements of εapproximation.

20.

Sharp distortion theorems for a subclass of closetoconvex mappings





Qinghua Xu Taishun Liu Xiaosong Liu《Frontiers of Mathematics in China》,2013年第8卷第6期


We introduce the class of strongly closetoconvex mappings of order c~ in the unit ball of a complex Banach space, and then, we give the sharp distortion theorems for this class of mappings in the unit ball of a complex Hilbert space X or the unit polydisc in Cn. As an application, a sharp growth theorem for strongly closetoconvex mappings of order α is obtained.
