Some properties of graphs of closed operators

In this paper we study some properties of graphs of closed operators in Hilbert spaces. We construct representations of von Neumann algebras induced by graphs of closed operators. We describe some classes of closed operators in terms of their characteristic matrices and study some properties of operations on graphs of closed operators.     

J—自共轭微分算子谱的定性分析

本文对J－自共轭微分算子谱理论研究情况做一些概要性的介绍,第一部分简要回顾了J－自共轭微分算子理论研究的发展过程,第二,三部分介绍了J－自共轭微分算子的本质谱和离散谱定性分析的主要方法和结论;第四部分扼要叙述J－自共轭微分算子其它方面的一些工作,以及J－自共轭微分算子谱理论研究中尚待解决的问题。     

Recurrent Linear Operators

We study the notion of recurrence and some of its variations for linear operators acting on Banach spaces. We characterize recurrence for several classes of linear operators such as weighted shifts, composition operators and multiplication operators on classical Banach spaces. We show that on separable complex Hilbert spaces the study of recurrent operators reduces, in many cases, to the study of unitary operators. Finally, we study the notion of product recurrence and state some relevant open questions.     

Localized Frames and Compactness

We introduce the concept of weak localization for continuous frames and use this concept to define a class of weakly localized operators. This class contains many important classes of operators, including: short time Fourier transform multipliers, Calderon–Toeplitz operators, Toeplitz operators on various functions spaces, Anti-Wick operators, some pseudodifferential operators, some Calderon–Zygmund operators, and many others. In this paper, we study the boundedness and compactness of weakly localized operators. In particular, we provide a characterization of compactness for weakly localized operators in terms of the behavior of their Berezin transforms.     

Heavy OWA Operators

We recall the OWA operator and discuss some of the features used to characterize these operators. In passing we introduce an new characterizing attribute called the divergence. We then consider two cases of information fusion and use these as motivation to generalize the OWA operator with the introduction of the Heavy OWA operator. These HOWA operators differ from the ordinary OWA operators by relaxing the constraints on the associated weighting vector. We consider some applications of these HOWA operators and provide some examples of weighting vectors associated with these HOWA operators.     

Sharp and weighted boundedness for multilinear operators associated with pseudo-differential operators on Morrey space

The paper proves some weighted boundedness for the multilinear operators related to some pseudo-differential operators on the generalized Morrey spaces by using the sharp function estimate of the multilinear operators.     

Hibert空间中广义框架的非交性

引入了Hilbert空间H中广义框架的非交性、强非交性,讨论了它们的一些性质;并且引入了保非交算子、强保非交算子,证明了酉算子、可逆算子是强保非交算子,下有界算子、余等距算子是保非交算子.     

A new approach to improve the order of approximation of the Bernstein operators: theory and applications

This paper presents a new approach to improve the order of approximation of the Bernstein operators. Three new operators of the Bernstein-type with the degree of approximations one, two, and three are obtained. Also, some theoretical results concerning the rate of convergence of the new operators are proved. Finally, some applications of the obtained operators such as approximation of functions and some new quadrature rules are introduced and the theoretical results are verified numerically.     

Surfaces Generation by Blending Interpolation on a Triangle with One Curved Side

We use some interpolation operators and some Bernstein type operators for construction of surfaces which satisfy some given conditions.     

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。     

Degree of approximation associated with some elliptic operators and its applications

The Jackson-type estimates by using some elliptic operators will be achieved. These results will be used to characterize the regularity of some elliptic operators by means of the approximation degree and the saturation class of the multivariate Bernstein operators as well.     

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。     

Some characterizations of almost Dunford–Pettis operators and applications

This paper attempts to deal with some characterizations of almost Dunford–Pettis operators from a Banach lattice into a Banach space. It also discusses some of the consequences derived from this study. As an application, we generalize some results of Meyer-Nieberg on the duality between semi-compact operators and order weakly compact operators.     

Fuzzy带算子环和Fuzzy带算理想

提出Fuzzy带算子环、Fuzzy带算理想和Fuzzy带算商环的定义,讨论它们的一些初等性质。     

Banach 空间上算子的几种不可约性

本文根据Cowen-Douglas 算子的定义引入两类与强不可约算子有紧密联系的算子类— B_n 算子与B 算子. 说明了在可分Banach 空间上存在B_n 算子与B 算子. 文章详细讨论了几种具有不可约性的算子类之间的关系并得到了一个关系图. 本文还给出这些算子类的一些性质, 包括算子的(拟) 相似不变性等.     

Convolution factorability of bilinear maps and integral representations

In this paper we consider a special class of continuous bilinear operators acting in a product of Banach algebras of integrable functions with convolution product. In the literature, these bilinear operators are called ‘zero product preserving’, and they may be considered as a generalization of Lamperti operators. We prove a factorization theorem for this class, which establishes that each zero product preserving bilinear operator factors through a subalgebra of absolutely integrable functions. We obtain also compactness and summability properties for these operators under the assumption of some classical properties for the range spaces, as the Dunford–Pettis property or the Schur property and we give integral representations by some concavity properties of operators. Finally, we give some applications for integral transforms, and an integral representation for Hilbert–Schmidt operators.     

Evolution semigroups and time operators on Banach spaces

We present new general methods to obtain shift representation of evolution semigroups defined on Banach spaces. We introduce the notion of time operator associated with a generalized shift on a Banach space and give some conditions under which time operators can be defined on an arbitrary Banach space. We also tackle the problem of scaling of time operators and obtain a general result about the existence of time operators on Banach spaces satisfying some geometric conditions. The last part of the paper contains some examples of explicit constructions of time operators on function spaces.     

Modular Convergence Theorems for Integral Operators in the Context of Filter Exhaustiveness and Applications

We prove some modular convergence theorems for nonlinear Urysohn-type integral operators, applying filter convergence of sequences of functions. We give some applications to Mellin operators, including moment, Mellin-Poisson-Cauchy and Mellin-Gauss-Weierstrass operators. We show that our results are proper extensions of the classical ones, and we pose an open problem.     

Continuity of Multilinear Operators in Weighted Herz Spaces with Extreme Exponents

Continuity is obtained of some multilinear operators related to certain integral operators for the weighted Herz spaces with extreme exponents. The operators include the Littlewood–Paley and Marcinkiewicz operators.