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．     

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。     

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．     

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.     

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.     

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.     

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.     

白噪声分析中的梯度算子和散度算子

在白噪声分析的框架中，我们给出了广义Weiner泛函空间上的梯度算子和散度算子的定义与公式，并利用梯度和散度算子以及适应投影建立了广义泛函的表示公式．也证明了积分核算子可用梯度与散度算子表出．     

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．     

A class of pseudo-monotone operators and its applications in PDE

In this paper we give a criterion of pseudo-monotone operators by which a class of operators related to elliptic partial differential equations is recognized as pseudo-monotone operators. Some applications in boundary value problems for elliptic equations and obstacle problems are given. Research supported by the Fund of IMAS     

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.     

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.     

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。     

On invertible contractions of quotients generated by a differential expression and by a nonnegative operator function

In the present paper, we describe invertible contractions of the maximal quotient generated by a differential expression with bounded operator coefficients and by a nonnegative operator function. We show that the operators inverse to such contractions are integral operators and prove a criterion for such operators to be holomorphic. Using the results obtained, we describe the generalized resolvents of symmetric quotients.     

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.     

COMPOSITION OPERATORS ON HARDY-ORLICZ SPACES

Properties of composition operators induced by analytic self-maps on the unit disk of the complex plane in Hardy-Orlicz spaces are discussed. Results are concerned about boundedness, invertibility, compactness, Fredholm operators and spectra of composition operators.     

ON CERTAIN PROPERTIES OF THE COMBINATIONS OF SZáSZ-DURRMEYER OPERATORS

In the present paper we study properties of Szász-Durrmeyer operators. These operators are introduced in [5] and generalize the integral operators proposed by S.M.Mazhar and V.Totik in [12]. We also generalize some results obtained by M. Heilmann[6] and D.-X. Zhou[16].     

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.     

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