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共有20条相似文献,以下是第1-20项 搜索用时 375 毫秒

1.  Three-space 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 λ-BCAP with conjugate operators if and only if the pair (X, Y) has the λ-BCAP 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.  ε-WEAKLY 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 c-weakly Chebyshev subspaces of Banach spaces. We will prove that all closed subspaces of a Banach space X are ε-weakly 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 ε-isometries 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 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.    

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.  Ball-covering 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 ball-covering 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 ball-covering property, if it admits a ball-covering consisting of countably many balls. This paper, by constructing the equivalent norms on l~∞, shows that ball-covering 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.  ε-PSEUDO 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 ε-pseudo Chebyshev and ε-quasi Chebyshev subspaces of Banach spaces. We will prove that a closed subspace W is ε-pseudo Chebyshev if and only if W is ε-quasi 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 Moore-Penrose inverses of lower triangular operator matrices are established. As an application, the explicit representations of Bott-Duffin 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 NON-COMPACT 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 non-compact 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 k-semi-stratifiable 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  
   Ren-zhongFeng Ren-hongWang《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 three-sided 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 Yuan-hong Li Rong-lu《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 F-WGHP, we introduce the UAK-property and find that this sort of property has close relationship with F-WGHP. In the course of discussing F-WGHP and WGHP of (C0)cn, we discuss the F-WGHP and WGHP of the almost-null 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 translation-invariant 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 ε-approximation.    

20.  Sharp distortion theorems for a subclass of close-to-convex 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 close-to-convex 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 close-to-convex mappings of order α is obtained.    

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