解析函数的Banach空间上之复合算子

本文研究了一类解析函数的Ｂａｎａｃｈ空间Ｘ上之复合算子，这类空间包含了Ｂｌｏｃｈ空间，并且可看作Ｂｅｒｇｍａｎ空间Ｌ１ａ（Ｄ）中具有原子分解的解析函数的对偶空间．我们刻划了这类空间上紧复合算子及Ｆｒｅｄｈｏｌｍ复合算子的特征，此外，还研究了具有闭值域的复合算子．     

冯·诺依曼代数的可测算子的性质

本文研究了冯·诺依曼代数的可测算子的基本性质,定义了阶梯算子,证明了任意一个正可测算子可以由阶梯算子在定义域内按照强算子拓扑逼近,从而证明了任意一个可测算子可以由投影在定义域内按照强算子拓扑逼近.此外,还讨论了可测算子与有界算子的复合算子的可测性.     

一类解析算子函数空间上的复合算子

本文用算子函数论的方法，研究了解析算子函数的Banach空间X，X0上的复合算子．给出此复合算子为有界的条件，并刻划了此复合算子在X0上为紧的特征．     

关于多个算子的Furuta型算子单调函数

设p≥1,且A、B是Hilbert空间上两个正算子,T.Furuta给出若A≥B>0,那么对任意t∈[0,1]有,G(r,s)=A-r/2{Ar/2(A-t/2BpA-t/2)sAr/2}1-t+r/(p-t)+srA-r/2是关于r,s在r≥t及s≥1上单调递减的,我们给出该结果可以推广到多个算子的情形.     

一类二阶与四阶微分算子积的自伴性

利用矩阵运算及算子的基本理论,讨论了由微分算式L_1=D~((2))+q_1(t)和L_2=D~((4))+q_2(t)其中(D=d/dx,t∈I=[a,b])生成的两个微分算子L_i(i=1,2)积L_1L_2的自伴性问题,并在常型情形下,获得了积算子自伴的充分必要条件.     

广义幂等算子差的可逆性

设P, Q为Hilbert空间H上的幂等算子, 关于算子$P$的广义幂等算子类ω(P)定义为ω(P)={A∈B}(H): A²=αA+βP, AP=PA=A,P²=P,∨α, β∈C}. 对任意A ∈ω(P), B∈ω(Q)使得A²=αA +βP, B²=mB+nQ,βn≠ 0, 得到了如下的结论: 值域R(PQ)是闭的充要条件是值域R(AB)是闭的; 如果P-Q是可逆的, 则A-B是可逆的.     

加权Bergman空间上的Toeplitz算子和Hankel算子

西方给出了Ｃ＾ｎ中单位球上的带权的Ｂｅｒｇｍａｎ空间上具一般符号的Ｔｏｅｐｌｉｔｚ算子和Ｈａｎｋｅｌ算子为紧的充要条件。     

一类无穷维Hamilton算子的Fredholm性及本质谱

讨论了一类无穷维Hamilton算子的Fredholm性,由于无穷维Hamilton算子是分块算子矩阵,将它的Fredholm性用它的元素算子的某种组合来描述,给出了无穷维Hamilton算子是Fredholm算子的充分必要条件.     

非游荡算子的性质*

本文研究一类具有混纯性质的线性算子:非游荡算子,该类算子仅在无穷维线性空间中.我们给出非游荡算子紧集上的超循环分解.     

Nilpotent operators similar to irreducible operators

We give a necessary and sufficient condition for the nilpotent operators to be similiar to irreducible operators, and give an answer to D. A. Herrero Conjectures for nilpotent operators.     

Disjointly homogeneous Banach lattices and compact products of operators

The notion of disjointly homogeneous Banach lattice is introduced. In these spaces every two disjoint sequences share equivalent subsequences. It is proved that on this class of Banach lattices the product of a regular AM-compact and a regular disjointly strictly singular operators is always a compact operator.     

广义弱亚正规算子的正规性

主要研究了T是广义弱亚正规算子时,T~t是拟正规算子的充要条件是T是拟正规算子.并且举例说明了存在非次正规的广义弱亚正规算子T使得T~t是次正规的.     

Operator Method of Solving Nonlinear Differential Equations

We discuss the possibility of applying linear structures for solving nonlinear differential equations.     

Fredholm Operators and Riesz Theory for Polynomially Compact Operators

In this article, we give a characterization of a class of bounded Fredholm operators on a Banach space which is developed to present some general existence results of the operators equation of the second kind. The obtained results are used to describe the Riesz–Schauder theory of compact operators in the more general setting of polynomially compact operators.     

Stable and stabilizable means involving linear operator arguments

In this paper we extend the stability and stabilizability concepts from the case that the variables are positive real numbers to the case that the variables are positive linear operators. Since the algebra of bounded linear operators is not commutative, such extension does not appear to be obvious. As applications, iterative operator algorithms, converging to some operator means, are discussed.     

对称算子的两种自伴延拓形式之间的联系

考虑了von Neumann形式的自伴延拓和以Calkin方法给出的自伴延拓之间的关系，证明了这两种自伴延拓是一致的并可以互相转化的.