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.     

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.     

本质正规算子的迹类算子扰动

本文利用ＢＤＦ定理以及构造技巧证明了关于本质正规算子的Ｐｅａｒｃｙ－Ｓａｌｉｎａｓ定理．作为此定理的应用，证明了本质正规算子可以通过迹类算子的小扰动成为不可约算子．     

一类新型非正规算子的谱分析

本文引入了一类新型非正规算子,即具复谱的u-标算子.证明了该类算子具有Jordan型分解,讨论了u-标算子与标型谱算子的关系,并通过例子说明了该类算子的构造.     

拟幂零积分算子的等价刻划

本给出了一娄具有非负核函数的积分算子，并得到了该算子为拟零算子的充必要条件，该算子包括了重要的Hardy算子。     

Unitary equivalence of one-parameter groups of Toeplitz and composition operators

The composition operators on H² whose symbols are hyperbolic automorphisms of the unit disk fixing ±1 comprise a one-parameter group and the analytic Toeplitz operators coming from covering maps of annuli centered at the origin whose radii are reciprocals also form a one-parameter group. Using the eigenvectors of the composition operators and of the adjoints of the Toeplitz operators, a direct unitary equivalence is found between the restrictions to zH² of the group of Toeplitz operators and the group of adjoints of these composition operators. On the other hand, it is shown that there is not a unitary equivalence of the groups of Toeplitz operators and the adjoints of the composition operators on the whole of H², but there is a similarity between them.     

Fixed points of generalized e-concave (generalized e-convex) operators and their applications

In this paper, we present the definitions of generalized e-concave operators and generalized e-convex operators, which are the generalizations of e-concave operators and e-convex operators, respectively. Without compactness or continuity assumption of generalized e-concave operators and generalized e-convex operators, we have proved the existence, uniqueness and monotone iterative techniques of their fixed points. Our results are even new to e-concave operators and e-convex operators. Finally, we apply the results to the singular boundary value problems for second order differential equations.     

多线性Littlewood—Paley算子在一类H^1空间上的加权有界性

本证明明了多线性Littlewood—Patey算子在一类H^1空间上的加权有界性。     

Toeplitz Operators on Dirichlet Spaces

In this paper we study Toeplitz operators on Dirichlet spaces and describe the boundedness and compactness of Toeplitz operators on Dirichlet spaces. Meanwhile, we give density theorems for Toeplitz operators on Dirichlet spaces Received December 22,1998, Revised March 27, 2000, Accepted June 27, 2000     

Essentially subnormal operators

An operator is essentially subnormal if its image in the Calkin algebra is subnormal. We shall characterize the essentially subnormal operators as those operators with an essentially normal extension. In fact, it is shown that an essentially subnormal operator has an extension of the form ``normal plus compact'.

The essential normal spectrum is defined and is used to characterize the essential isometries. It is shown that every essentially subnormal operator may be decomposed as the direct sum of a subnormal operator and some irreducible essentially subnormal operators. An essential version of Putnam's Inequality is proven for these operators. Also, it is shown that essential normality is a similarity invariant within the class of essentially subnormal operators. The class of essentially hyponormal operators is also briefly discussed and several examples of essentially subnormal operators are given.

     

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．     

Positive set‐operators of low complexity

The powerset operator, ??, is compared with other operators of similar type and logical complexity. Namely we examine positive operators whose defining formula has a canonical form containing at most a string of universal quantifiers. We call them ?‐operators. The question we address in this paper is: How is the class of ?‐operators generated ? It is shown that every positive ?‐operator Γ such that Γ(??) ≠ ??, is finitely generated from ??, the identity operator Id, constant operators and certain trivial ones by composition, ∪ and ∩. This extends results of [3] concerning bounded positive operators.     

Bergman空间上Toeplitz算子的凸性

本文讨论了Ｂｅｒｇｍａｎ空间上Ｔｏｅｐｌｉｔｚ算子的凸性，证明了具有调和符号和一类连续函数符号的Ｔｏｅｐｌｉｔｚ算子是凸型算子，并举例说明，存在具有连续函数符号的非凸型Ｔｏｅｐｌｉｔｚ算子。     

Toeplitz and composition operators on H2 (B n)

The composition operators with closed rangc on H²(B _n) are characterized, and the Fredholmness of products of Toeplitz and composition operators discussed. Moreover, using composition operators, the spectra of Toeplitz operators are studied. Project supported by the National Natural Sciencc Foundation of China and the Postdoctoral Science Foundation of China.     

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．     

Bergman空间上Toeplitz算子的局部及Fredholm性质

本文讨论了Ｂｅｒｇｍａｎ空间上Ｔｏｅｐｌｉｔｚ算子的局部谱的关系．利用局部化原理给出了Ｔｏｅｐｌｉｔｚ算子拟换位子紧性的一个充分条件．给出了一类符号的Ｔｏｅｐｌｉｔｚ算子是Ｆｒｅｄｈｏｌｍ算子的充分条件．     

组合线性算子

本文给出一种构造组合线性逼近算子的方法，由此可得到具有特殊逼近性质的线性算子．     

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.     

An asymmetric Putnam-Fuglede theorem for unbounded operators

The intertwining relations between cosubnormal and closed hyponormal (resp. cohyponormal and closed subnormal) operators are studied. In particular, an asymmetric Putnam-Fuglede theorem for unbounded operators is proved.