Banach空间上闭线性子空间强正交可补的充分必要条件

证明了闭的极大线性子空间是强正交可补的充分必要条件是,空间X是自反严格凸的.     

闭极大线性子空间正交补的判别及应用

继续前面的工作,证得对于赋范线性空间中固定线性子空间成为迫近子空间的充分必要条件.特别的,对于闭极大线性子空间来说,的迫近性等价于的正交可补性.做为其直接推论,给出Banach空间成为自反空间的5个等价条件,其中4个条件为经典结果,一个条件为已有文献中给出的条件,但给出全新的证明.     

广义正交分解定理与Tseng度量广义逆

本文将Banach空间中广义正交分解定理从线性子空间拓广至非线性集—太阳集,分别给出了一算子为度量投影算子和一度量投影算子为有界线性算子的充要条件;得到了判别Banach空间中子空间广义正交可补的充要条件;建立了王玉文和季大琴(2000年)新近引入的Banach空间中的线性算子的Tseng度量广义逆存在的特征刻划条件;这些工作本质地把王玉文等人的新近结果从自反空间拓广至非自反空间的情形.     

广义正交分解定理与Tseng度量广义逆

本文将Banach空间中广义正交分解定理从线性子空间拓广至非线性集太阳集,分别给出了一算子为度量投影算子和一度量投影算子为有界线性算子的充要条件;得到了判别Banach空间中子空间广义正交可补的充要条件;建立了王玉文和季大琴(2000年)新近引入的Banach空间中的线性算子的Tseng度量广义逆存在的特征刻划条件;这些工作本质地把王玉文等人的新近结果从自反空间拓广至非自反空间的情形.     

Banach空间抽象线性脉冲方程的可解范围

本文在一船Ｂａｎａｃｈ空间Ｘ上研究抽象线性脉冲方程的可解范围，其中Ａ是闭线性算子，文中构造了Ｘ的一个线性子空间Ｖ且在Ｖ上定义范数成为Ｂａｎａｃｈ空间，Ａ限制在Ｖ上生成指数衰减的强连续双半群，从而表明方程在Ｖ上可解，并证明Ｖ是方程可解的极大范围。     

Banach 空间中广义正交与度量投影

本文利用广义正交(“⊥”)这一工具,给出了在不自反的Banach空间中多值算子P为集值度量投影PL的充要条件是(i)P-1(0)=L(⊥),(ii)x∈X,y∈L,P(x y)=P(x) y,我们的结果推广了文[2]的在自反空间中且P为单值度量投影的相应结论;还得到了L(⊥)为线性子空间的充要条件是PL为有界线性算子;进而得到了L广义正交拓扑可补的充要条件是PL为有界线性算子,丰富了文[1,9]的结论.     

析函数的(FN)-代数中的闭理想问题

本文讨论了解析函数的(FN)-代数A0P中的闭理想问题,利用射影加权系给出了一个闭理想成为A0P中的补子空间的判别准则.     

非局部凸拓扑线性空间中的Hahn Banach延拓性

1 序 众所周知,Hahn(1926)和Banach(1929)曾经在赋范空间中给出过一个十分重要的有关连续线性泛函的延拓定理: H.-B.定理 设X为赋范空间,X_0为X的一个线性子空间,那么,对任意连续线性泛函     

解析函数的加权代数中的闭理想问题

该文讨论了单位圆盘上解析函数的加权代数犃犘中的闭理想问题,并且利用加权系给出了一个闭理想成为犃犘中的补子空间的判断准则     

Alth?fer-Sillke不等式的改进（英）

在本文中给出二元向量空间的子集的平均Hamming距离的一个新的下界和上界，这些界对于二元向量空间的线性子空间是紧的，且改进了[2]文的Alth?fer- Sillke不等式，从而部分解决了Ahlswede和Katona在[1]中提出的一个问题.     

Convergence of minimum norm elements of projections and intersections of nested affine spaces in Hilbert space

We consider a Hilbert space, an orthogonal projection onto a closed subspace and a sequence of downwardly directed affine spaces. We give sufficient conditions for the projection of the intersection of the affine spaces into the closed subspace to be equal to the intersection of their projections. Under a closure assumption, one such (necessary and) sufficient condition is that summation and intersection commute between the orthogonal complement of the closed subspace, and the subspaces corresponding to the affine spaces. Another sufficient condition is that the cosines of the angles between the orthogonal complement of the closed subspace, and the subspaces corresponding to the affine spaces, be bounded away from one. Our results are then applied to a general infinite horizon, positive semi-definite, linear quadratic mathematical programming problem. Specifically, under suitable conditions, we show that optimal solutions exist and, modulo those feasible solutions with zero objective value, they are limits of optimal solutions to finite-dimensional truncations of the original problem.     

THEORY OF SPECTRAL DECOMPOSITIONS WITH RESPECT TO THE IDENTITY FOR CLOSED OPERATORS

In this paper,the auther discusses some properties of closed operators acting on aBanach space with the spectral decomposition property with respect to the identity(abbrev.SDI).First,some equivalent conditions are given for a closed operator T to have the SDI.Next,for every hyperinvariant subspace Y of T with the SDI,it is proved that thecoinduced operator=T/Y has the SDI.Finally,properties of maximal nets of hyperinva-riant subspaces are discussed.     

The α-orthogonal complements of regular Dirichlet subspaces for one-dimensional Brownian motion

Roughly speaking a regular Dirichlet subspace of a Dirichlet form is a subspace which is also a regular Dirichlet form on the same state space. In particular, the domain of regular Dirichlet subspace is a closed subspace of the Hilbert space induced by the domain and α-inner product of original Dirichlet form. We investigate the orthogonal complement of regular Dirichlet subspace for one-dimensional Brownian motion in this paper. Our main results indicate that this orthogonal complement has a very close connection with theα-harmonic equation under Neumann type condition.     

Wavelet frames for (not necessarily reducing) affine subspaces II: The structure of affine subspaces

This is a continuation of the investigation into the theory of wavelet frames for general affine subspaces. The main focus of this paper is on the structural properties of affine subspaces. We show that every affine subspace is the orthogonal direct sum of at most three purely non-reducing subspaces, while every reducing subspace (with respect to the dilation and translation operators) is the orthogonal direct sum of two purely non-reducing ones. This result is obtained through considering the basic question as to when the orthogonal complement of an affine subspace in another one is still affine. Motivated by the fundamental question as to whether every affine subspace is singly-generated, and by a recent result that every singly generated purely non-reducing subspace admits a singly generated wavelet frame, we prove that every affine subspace can be decomposed into the direct sum of a singly generated affine subspace and some space of “small size”. As a consequence we establish a connection between the above mentioned two questions.     

Dense computability structures

We examine computability structures on a metric space and the relationships between maximal, separable and dense computability structures. We prove that in a computable metric space which has the effective covering property and compact closed balls for a given computable sequence which is a metric basis there exists a unique maximal computability structure which contains that sequence. Furthermore, we prove that each maximal computability structure on a convex subspace of Euclidean space is dense. We also examine subspaces of Euclidean space on which each dense maximal computability structure is separable and prove that spheres, boundaries of simplices and conics are such spaces.     

Invariant Maximal Positive Subspaces and Polar Decompositions

It is proved that invertible operators on a Krein space which have an invariant maximal uniformly positive subspace and map its orthogonal complement into a nonnegative subspace allow polar decompositions with additional spectral properties. As a corollary, several classes of Krein space operators are shown to allow polar decompositions. An example in a finite dimensional Krein space shows that there exist dissipative operators that do not allow polar decompositions.     

The finite-dimensional decomposition property in non-Archimedean Banach spaces

A non-Archimedean Banach space has the orthogonal finite-dimensional decomposition property（OFDDP） if it is the orthogonal direct sum of a sequence of finite-dimensional subspaces.This property has an influence in the non-Archimedean Grothendieck＇s approximation theory,where an open problem is the following： Let E be a non-Archimedean Banach space of countable type with the OFDDP and let D be a closed subspace of E.Does D have the OFDDP？ In this paper we give a negative answer to this question; we construct a Banach space of countable type with the OFDDP having a one-codimensional subspace without the OFDDP.Next we prove that,however,for certain classes of Banach spaces of countable type,the OFDDP is preserved by taking finite-codimensional subspaces.     

Maximal Points of Stable and Related Polynomials

We prove that any polynomial having all its roots in a closed half-plane, whose boundary contains the origin, has either one or two maximal points, and only one if it has at least one root in the open half-plane. This result concerns stable polynomials as well as polynomials having only real roots, including real orthogonal polynomials.     

Low Cohomogeneity Representations and Orbit Maximal Actions

An orthogonal representation of a compact Lie group is called polar if thereexists a linear subspace which meets all orbits orthogonally.It has been shown by Conlon that one can associate a Coxeter groupto such a representation.From this, an upper bound for the cohomogeneity of an irreduciblepolar representation can be derived.Another property of irreducible polar representations isthat the action restricted to the unit spherehas maximal orbits in the sense that any action having largerorbits is transitive.We give a classification of orbit maximal actions on spheresand use it to show that irreducible polar representations arecharacterized by these two properties.