On the Uniqueness of Isosceles Orthogonality in Normed Linear Spaces

Via studying the relation between isosceles orthogonality and the lengths of segments contained in the unit sphere, existing results on the uniqueness of isosceles orthogonality are improved.     

赋β-范空间中单位球面间的等距算子的线性延拓

本文得到了等距映射的线性延拓的一般结果:设E,F是赋范(或β-严格凸赋β-范)线性空间,若V_0:S_1(E)→S_1(F)是等距,且对任意的x,y∈S_1(E),有‖V_0x-|(?)|V_0y‖≤‖x-|(?)|y‖,(?)∈R,则V_0必可延拓到全空间上等距算子(或线性等距算子)。特别,当E,F是赋范线性空间,V_0是满射或F为严格凸空间时,则V_0必可延拓为全空间的线性等距算子,从而推广了文[3～5]中的相应结果。     

线性空间中的共逼近

本文研究了在局部凸空间和赋范线性空间中的（f-）共逼近和强（f-）共逼近的一些性质,给出了f-共逼近、强f-共逼近和强f-Kolmogorov集的特征定理.并举例说明G.S.Rao的两主要定理是不正确的,同时作了相应的更正.所得的结果中的部分推广和改进了Song、Rao和Narang等人的相应结果.     

点传递线性空间

本文是关于点传递线性空间的一个分类工作. 设${\mathcal{S}}$是一个点数为51的正则线性空间,其线长为6, $G$ 是${\cal S}$的一个自同构群.本文证明了群$G$不可能点传递.     

The Basic Principles for Stable Approximations to Orthogonal Generalized Inverses of Linear Operators in Hilbert Spaces

This work presents some basic principles concerned with two general settings for stable approximating orthogonal generalized inverses in Hilbert spaces. In these two settings, perfect convergence and perfect uniform convergence are two important concepts for making theoretical or numerical analysis. Our basic principles characterize the two important concepts by some necessary conditions: stability with other compensated conditions. These basic principles include as simple corollaries some well-known results.     

赋β-范空间中的最佳逼近问题

This paper deals with the problems of best approximation in β-normed spaces.With the tool of conjugate cone introduced in [1] and via the Hahn-Banach extension theorem of β-subseminorm in [2],the characteristics that an element in a closed subspace is the best approximation are given in Section 2.It is obtained in Section 3 that all convex sets or subspaces of a β-normed space are semi-Chebyshev if and only if the space is itself strictly convex.The fact that every finite dimensional subspace of a strictly convex β-normed space must be Chebyshev is proved at last.     

Stability Constants in Linear Spaces

We investigate the stability constants of convex sets in linear spaces. We prove that the stability constants of affinity and of the Jensen equation are of the same order of magnitude for every convex set in arbitrary linear spaces, even for functions mapping into an arbitrary Banach space. We also show that the second Whitney constant corresponding to the bounded functions equals half of the stability constant of the Jensen equation whenever the latter is finite. We show that if a convex set contains arbitrarily long segments in every direction, then its Jensen and Whitney constants are uniformly bounded. We prove a result that reduces the investigation of the stability constants to the case when the underlying set is the unit ball of a Banach space. As an application we prove that if D is convex and every δ-Jensen function on D differs from a Jensen function by a bounded function, then the stability constants of D are finite.     

Orthogonal Elements in Nonseparable Rearrangement Invariant Spaces

Doklady Mathematics - Let E be a nonseparable rearrangement invariant space, and let E0 denote the closure of the set of all bounded functions in E. We study elements of E orthogonal to the...     

Finite Linear Spaces II

Batten and Beutelspacher have characterized Finite Linear Spaces with lines of size n,n + 1 and n + 2, and with v (n + 1)²for n 22, and some of the cases for smaller n. In this article, using the structuredapproach we presented in our earlier article [8], we complete this characterization for smalln.     

关于仿射线性相关性的探讨

在线性空间中引入了仿射线性相关的概念,给出了它的特征刻画及若干重要性质,并用仿射线性相关性刻画了非齐线性方程组解的结构。     

Some p-Ranks Related to Orthogonal Spaces

We determine the p-rank of the incidence matrix of hyperplanes of PG(n, p ^e) and points of a nondegenerate quadric. This yields new bounds for ovoids and the size of caps in finite orthogonal spaces. In particular, we show the nonexistence of ovoids in and . We also give slightly weaker bounds for more general finite classical polar spaces. Another application is the determination of certain explicit bases for the code of PG(2, p) using secants, or tangents and passants, of a nondegenerate conic.     

特征为2的有限正交空间上全奇异子空间的Critical问题

利用特征为2的有限正交空间的性质及计数定理在特征为2的有限正交空间上研究了全奇异子空间的Critical问题,得到了相应的计数公式和Critical指数.     

Linear Isometries of S~p Spaces

Abstract This paper gencralizes the result about linear isometries of S~ spaces given by W.P.Novingerand D.M.Oberlin[2]for the unite dise of C to the bounded symmetric domains of C~n     

Linear Isometries of S^D Spaces

This paper generalizes the result about linear isometries of S^pspaces given by W.P.Novinger and D.M.Oberlin[2] for the unite dise of C to the bounded symmetrie domains of C^n。