Hilbert空间上两个正交射影的乘积

该文研究Hilbert空间H上正则射影对(P,Q)的性质和结构,给出H上有界线性算子A表示为两个正交射影乘积的充分必要条件.     

关于Hilbert空间子空间的维数

本义对 Ｈｉｌｂｅｒｔ空间的子空间的一种维数［３］给出了一种表示方法，并讨论了它的一些性质     

两个正交射影差的范数不等式

设H是一个希尔伯特空间,B(H)表示H上有界线性算子全体构成的集合.P,Q∈B(H)是两个正交射影.运用算子分块技巧给出了||PX-XQ||的一个刻画,在此基础上证明了不等式||P-Q||≤1.进一步运用算子分块技巧与算子谱理论,给出||P-Q||=1以及严格不等式成立的充分条件.最后给出P-Q可逆的一个等价刻画.     

复射影空间中复子流形的一点注记

复射影空间中复子流形的一点注记曹锡芳（杨州师范学院数学系，２２５００２）关键词复射影空间，截面曲率．分类号ＡＭｓ（１９９１）５３Ｃ５５，５３Ｃ４２／ＣＣＬＯ１８６．１６设ＣＰ￣（ｎ＋ｐ）是具有Ｆｕｂｉｎｉ－ｓｔｕｄｙ度量的复ｎ＋ｐ维射影空间，它的常数...     

关于Suzuki群与射影平面的一个注记

设G Aut(D)且Soc(G) =Sz(q) ,这里q=2 p,p为奇素数,若有Sz(q) 相似文献   

Hilbert空间子空间的维数和半Fredholm算子的指标

对Hilbert空间H中的任意子空间,引入了一种广义维数并使其全序化.发现了可列个无限维数:∞~*<∞ⁿ<∞^m,其中n,m为整数且n>m.由此定义了半Fredholm算子SF(H)的广义指标.证明任意纯半Fredholm算子A∈SF₊(H)(SF_-(H))有Ind_gA=∞^*(-∞^*).这里的广义维数和指标是几何与拓扑的概念,像有限维数和Fredholm指标一样具有某些分析演算功能.作为例,证明了:对任意等距算子V₁,V₂,它们在H上左可逆算子B_i^x(H)中道路连通当且仅当Ind_gV₁=Ind_gV₂.从而推出,(?) A,B∈SF₊(H)(SF_-(H)),它们为道路连通的充要条件为Ind_gA=Ind_gB.其余有关SF(H)的结果,如指标经紧和小扰动的稳定性,Ind_g:SF(H)→ZU{-∞^*,∞^*}连续皆成立.     

概率空间上的分形性质

设（Ω,Ｆ,μ）为一概率空间,｛ｘｎ,ｎ≥１｝是定义在（Ω,Ｆ,μ）上的随机过程,Ｅ为β的任意子集,ｄｉｍμ（Ｅ）和Ｄｉｍμ（Ｅ）分别为Ｅ的Ｈａｕｓｄｏｒｆｆ和Ｐａｃｋｏｎｇ维数,若ｄｉｍμ（Ｅ）＝Ｄｉｍμ（Ｅ）,则称Ｅ是正则集。     

Hilbert空间H中带符号广义框架的一个刻画

本文研究了可分的Hilbert空间H中带符号广义框架,利用算子理论方法,给出了H中一族向量{hm}m∈M是一个带符号广义框架当且仅当带符号广义框架的框架算子的正部S 和负部S-是有界线性算子,讨论了H中带符号广义框架的框架算子S的可逆性,并且得到了H中每个向量f关于带符号广义框架{hm}m∈M和其对偶带符号广义框架{~hm}m∈M的表示式.     

强正则自补图的一个注记

Kotzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongly-regular self- complementary graph whose order is 4k 1, where 4k 1=x2 y2, x and y are positive integers; what is the minimum number that made there exist at least two non-isomorphic strongly-regular self-complementary graphs. In this paper, we use two famous lemmas to generalize the existential conditions for strongly-regular self-complementary circular graphs with 4k 1 orders.     

$c$-半层空间与几乎完全正则空间一点注记

In this paper, we give some characterizations of almost completely regular spaces and c-semistratifiable spaces(CSS) by semi-continuous functions. We mainly show that:(1)Let X be a space. Then the following statements are equivalent:(i) X is almost completely regular.(ii) Every two disjoint subsets of X, one of which is compact and the other is regular closed, are completely separated.(iii) If g, h : X → I, g is compact-like, h is normal lower semicontinuous, and g ≤ h, then there exists a continuous function f : X → I such that g ≤ f ≤ h;and(2) Let X be a space. Then the following statements are equivalent:(a) X is CSS;(b) There is an operator U assigning to a decreasing sequence of compact sets(Fj)j∈N,a decreasing sequence of open sets(U(n,(Fj)))n∈N such that(b1) Fn■U(n,(Fj)) for each n ∈ N;(b2)∩n∈NU(n,(Fj)) =∩n∈NFn;(b3) Given two decreasing sequences of compact sets(Fj)j∈N and(Ej)j∈N such that Fn■Enfor each n ∈ N, then U(n,(Fj))■U(n,(Ej)) for each n ∈ N;(c) There is an operator Φ : LCL(X, I) → USC(X, I) such that, for any h ∈ LCL(X, I),0 Φ(h) h, and 0 Φ(h)(x) h(x) whenever h(x) 0.     

关于拟正则半环上可除半环同余的注记

研究了拟正则半环上的同余,给出了拟正则半环上一类理想的性质,并利用这类理想给出了拟正则半环上可除半环同余的几种等价形式.     

Projections in operator ranges

If is a Hilbert space, is a positive bounded linear operator on and is a closed subspace of , the relative position between and establishes a notion of compatibility. We show that the compatibility of is equivalent to the existence of a convenient orthogonal projection in the operator range with its canonical Hilbertian structure.

     

正交投影的积与差的Moore-Penrose逆

运用分块算子矩阵的方法,给出了HIlbert空间上两个正交投影的和与差的Moore-Penrose逆的一个新的表达式.     

On Sums of Projections

In the paper, for all n, we describe the set _n of all real numbers admitting a collection of projections P ₁,...,P _n on a Hilbert space H such that _k=1 ⁿ P _k= I (I is the identity operator on H) and study the problem to find all collections of this kind for a given _n .     

A Note on a Problem of M. S. Berger

In this paper, we discuss the problem concerning global and local structure of solutions of an operator equation posed by M. S. Berger. Let f : U (?)E→ F be a C1 map, where E and F are Banach spaces and U is open in E. We show that the solution set of the equation f(x)=y for a fixed generalized regular value y of f is represented as a union of disjoint connected C1 Banach submanifolds of U, each of which has a dimension and its tangent space is given. In particular, a characterization of the isolated solutions of the equation f(x) = y is obtained.     

正交射影在广义框架理论中的应用

本文研究了可分的Hilbert空间H中的广义框架,运用算子理论方法,研究了可分的 Hilbert空间H中广义框架的性质,给出了广义框架的对偶广义框架的一些刻画,并且证明了两个广义框架是强非交的一个充分必要条件．     

A Note on Metric Projections

In this note we give an example of a strictly convex, reflexive, smooth Banach space which has a Chebyshev subspace M, such that the projection onto M is linear and has norm equal to 2. Moreover, we give necessary and sufficient conditions on a space so that every projection has norm less than a constant which is less than 2.