Pontrjagin空间上一般算子代数弱闭和一致闭的等价条件

本文研究Pontrjagin空间上一般算子代数弱闭和一致闭的等价条件,得到定理:设C0(U),C1(U,L,R,D,V),C2a(U),C2b(U,R),C3a(U),C3b(U,R)分别是Ⅱk空间上第0,Ⅰ,Ⅱa,Ⅱb,Ⅲa和Ⅲb类的算子代数,则(1)C0(U),C2a(U)或C3a(U)为一致闭(弱闭)的等价条件是U是Hibert空间G上的C*-代数(W*-代数;(2)C1(U,L,R,D,V)为一致闭(弱闭)的等价条件是U是Hibert空间H上的C*-代数(W*-代数),并且R是闭子空间,V是闭算子,L对称闭的;(3)C2b(U,R)或C3b(U,R)为一致闭(弱闭)的等价条件是U是Hibert空间H上的C*-代数(W*-代数),并且R是闭子空间．     

Pontrjagin空间上算子代数理想的结构

对Π_k空间上一般对称算子代数,给出了对称理想的结构的两个结果．(1)令A是Π_k空间上一般对称算子代数．若M_1∩M_2≠{0},则存在对■~((k))不变的子空间V∈~(k)H~(k),满足M_1∩M_2=F(V) J,这里J=(■),T属于k×k矩阵代数,V=(R){VXX│X∈D},R和R⊥是对*-算子代数A_p~(k)不变的．(2)令A是Π_k空间上一般对称算子代数．设△=M_1∩M_2≠{0}．则M_2：△ U(Q),其中U(Q)是下列元的集(■),这里B∈A_p,q_i是算子代数U到R~⊥的线性映射,并满足条件：q(A B)=Aq(B),A,B∈A_p．     

Hilbert空间H上正交射影对的一个注记

本文研究了Hilbert空间H上正则射影对的性质和结构，证明了酉算子V与正交射影对（P，Q）交织（i．e．，VP=QV，PV=VQ）的充分必要条件是dim（R（P）∩N（Q））=dim（N（P）∩R（Q）），给出了满足上述条件均酉算子V均一般形式．     

关于线性变换的像空间与核空间的直和

讨论数域P上有限维线性空间V上线性变换A的方幂A~k的像空间ImA~k与核空间KerA~k的直和,并将结论推广到无限维线性空间.证明了:V=ImA~k+KerA~k当且仅当ImA~k=ImA~(k+1),以及ImA~k∩KerA~k=0当且仅当KerA~k=KerA~(k+1).     

一类非线性算子方程的求解方法

1.引言首先研究线性方程Au=f (1.1)的求解问题,其中A是H→H的连续线性算子,H是可分Hilbert空间,U,f∈H,||f||=1.利用得到的结论,研究一类非线性算子方程AuBu+Cu=f(1.2)     

弱闭T(N)-模中Cp空间的等距映射

刻划了弱闭T(N)-模中Schatten类之间的等距线性满映射.设U、W分别为由左连续序同态N→和N→所确定的弱闭T(N)-模.Φ为U∩Cp到W∩Cp(1≤p<∞,p≠2)上的等距线性映射.若(0)+=(0),H-=H且min{dim(0),dim(0)#,dim(HH～),dim(HH∧)}≥2,则存在到的等距Ui(i=1,2)及酉算子Vi(i=1,2),使得Φ(A)=U1AV1或Φ(A)=V2AU2.     

Banach空间中拟线性投影算子

证明了 :在自反 Banach空间＄X＄中 ,每个闭子空间 L,都存在 X到 L上的拟线性投影算子 SL.一般说来 ,SL 既非度量投影算子 ,又非线性算子 .     

李超代数的c-可补子代数(英文)

李超代数L的一个子代数B称为c-可补的,若存在L的一个理想B使得L=B+C和B∩C(?)B_L,此处B_L是包含在B且为L的理想中最大的一个,本文把c-可补子代数理论发展到李超代数,并利用它们得到了可解李超代数的一些刻画.同时也得到了E-李超代数的一些性质.     

Hilbert空间上线性算子广义逆A_(T,S)~((2))的存在性及其表示式

设H1和H2是两个Hilbert空间,B(H1,H2)表示从H1到H2的所有有界线性算子的集合,T和S分别是H1和H2的两个闭子空间．如果存在线性算子X∈B(H2,H1)满足XAX=X,R(X)=T,N(X)=S,则称X为线性算子A的具有指定像空间T和零空间S的外逆,记为AT,S(2)．该文进一步研究了线性算子广义逆AT,S(2)存在的若干等价条件及其性质,建立了算子广义逆AT,S(2)的表示形式．     

Riesz Transforms Associated with Schrdinger Operators Acting on Weighted Hardy Spaces

Let L =-? + V be a Schrdinger operator acting on L2(Rn), n ≥ 1, where V ≡ 0 is a nonnegative locally integrable function on Rn. In this article, we will intropduce weighted Hardy spaces H L(w) associated with L by means of the square function and then study their atomic decomposition theory. We will also show that the Riesz transform ?L-1/2associated with L is bounded from our new space Hp L(w) to the classical weighted Hardy space Hp(w) when n/(n +1) p 1 and w ∈ A1∩ RH(2/p)′.     

向量空间中拟不变元素的结构

设Ｖ是有限域上Ｆ的向量空间,Ｇ是Ｖ上的线性变换群．本文讨论了Ｖ中拟不变元素的结构·即如果Ｕ是Ｖ中的拟不变元,则存在ｇ∈Ｇ,使得Ｕ∩ｇ（Ｕ）是Ｇ-不变的,或存在ｘ∈ Ｖ＼Ｕ,使得 Ｖ＋是 Ｇ不变的．     

关于图的L(2,1)标号核图

图的L(2,1)标号核图来自频率分配问题而导致的图论问题.在本文中,我们证得(i)对任意简单图G,存在G的一个标号核图Gcore,使得L(G)=L(Gcore)和L(G)≥|V(Gcore)|-1;(ii)设图G有p个顶点且边集|E(G)|≠φ,存在路 Pi G(1≤i≤m)和路Hs G(1≤s≤n),其中在G中V(Pi)∩V(Pj)=φ(i≠j),在G中V(P,)∩V(Pt)=φ(s≠t),则有m∑t=1|V(Pt)|+n∑s=1|V(Hs)|-(m+n)≥p;(iii)G是p(p≥5)个顶点的简单图,则有p+3≤L(G)+L(G)≤3p-4.     

An intersection theorem for multivalued maps

LetE be a Banach space and letV, W ? E be two closed subspaces such thatE=V ⊕ W. LetF, G: E-· E be two multivalued maps. The problem we are concerned with is to give conditions onF andG ensuring the nonemptiness ofF(V) ∩ G(W).     

∑＊-嵌入子群对有限群的可解性的影响

设H是有限群G的子群, K/L是G的任一非Frattini主因子.如果对每一满足L≤A＜B≤K且A是B的极大子群的子群对（A,B）,都有HA=HB或者H∩A=H∩B,则称H是G的∑＊-嵌入子群.通过有限群G的某些子群的∑＊-嵌入性,给出了一些有限群G的正规子群为可解群的一些判别条件,推广了已有的一些结论.     

On principal invariant subspaces

Let F and G be closed subspaces of the complex Hilbert space H, and U and V be closed subspaces of F and G, respectively. In this paper, using the technique of operator block, we present the necessary and sufficient conditions under which (U, V) is a pair of (strictly, non-degenerate) principal invariant subspaces for (F, G).     

SPECTRAL GAP SOLUTIONS OF THE DISSIPATIVE KIRCHHOFF EQUATION

§1. Introduction This paper is devoted to the question of the global solvability of the dissipative Kirch-ho? equation ?t u ? m 2 | x u|2dx x u δ?tu = 0 (x ∈?, t > 0), …     

CHARACTERIZATIONS OF JORDAN (?)-SKEW MULTIPLICATIVE MAPS ON OPERATOR ALGEBRAS OF INDEFINITE INNER PRODUCT SPACES

Let H and K be indefinite inner product spaces. This paper shows that a bijective map φ:B(H)→B(K) satisfies φ(AB B A) =φ(A)φ(5) φ(B) φ(A) for every pair A,B ∈B(H) if and only if either φ(A) = cU AU for all A or φ(A) = cUA U for all A; φsatisfies φ(AB A) = φ(A)φ(B) φ(A) for every pair A,B ∈B(H) if and only if either φ(A) = UAV for all A or φ(A) = UA V for all A, where A denotes the indefinite conjugate of A, U and V are bounded invertible linear or conjugate linear operators with U U = c-1I and V V = cI for some nonzero real number c.     

Invariance of dimension of p-subspaces in bernstein algebras *

The purpose of this paper is to prove that some vector subspaces, called p-subspaces, obtained from the Peirce decomposition of a Bernstein algebra A relative to an idempotent have dimensions which are independent of the idempotent used to decompose A. In particular, for Bernstein-Jordan algebras, this fact is true for every such subspace and this implies that all p-subspaces of a Bernstein algebra, contained in V, for A = Ke + U + V, have invariant dimension. Finally we classify all p-subspaces of degree ≥ 3, contained in U, in a Bernstein algebra A, relative to the invariance (or not) of dimension.     

Characterization of the Transformation Group of the Space of a Null System

In the space I_r of the invariant r-dimensional subspaces of a null system in (2r +1)-dimensional projective space, W.L. Chow characterized the basic group of transformations of I_r as all the transformations φ: I_r → I_r which are bijective and such that φ and φ^?1 preserve adjacency. In the present paper we examine arbitrary mappings φ of I_r which satisfy the two conditions: 1. φ preserves adjacency. 2. For any a ∈ I_r there exists b ∈ I_r such that a^φ ∩ b^φ = ø.