ON THE ESSENTIAL SPECTRUM OF PSEUDODIFFERENTIAL OPERATORS （Ⅱ）

This paper coutinues the studies of the essential spectrum of nonsemi-bounded pseudodifferential operators. The author improves the results in [5] in some sense. For the relativistic Schrodinger operator,√(-Δ+m^2)+v(x),complete results are obtained.     

闭算子Moore-Penrose逆的逆序律(英文)

In this paper, the reverse order law for the Moore-Penrose inverse of closed linear operators with closed range is investigated by virtue of the Norm-preserving extension of the bounded linear operators. The results generalize some results obtained by S Izumino in [12].     

关于α-Bernstein算子Voronovskaja定理的注记（英文）

The α-Bernstein operators possess similar approximation properties to the classic Bernstein operators.The main purpose of this note is to introduce another form of Voronovskaja theorem for the linear positive operators and provide a proof of the restricted version of the theorem,which takes very little time to describe.     

THE LERAY-SCHAUDER CONDITION FOR 1-SET WEAKLY-CONTRACTIVE AND （ws）-COMPACT OPERATORS

Abstract The main purpose of this article is to prove a collection of new nxea point theorems for （ws）-compact and so-called 1-set weakly contractive operators under Leray- Schauder boundary condition. We also introduce the concept of semi-closed operator at the origin and obtain a series of new fixed point theorems for such class of operators. As consequences, we get new fixed point existence for （ws）-compact （in particular nonexpansive） self mappings unbounded closed convex subset of Banach spaces. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness. Later on, we give an application to generalized Hammerstein type integral equations.     

ON THE GENERALIZED RESOLVENT OF LINEAR PENCILS IN BANACH SPACES

Utilizing the stability characterizations of generalized inverses of linear operator, we investigate the existence of generalized resolvent of linear pencils in Banach spaces. Some practical criterions for the existence of generalized resolvents of the linear pencil λ→ T λ S are provided and an explicit expression of the generalized resolvent is also given. As applications, the characterization for the Moore-Penrose inverse of the linear pencil to be its generalized resolvent and the existence of the generalized resolvents of linear pencils of finite rank operators, Fredholm operators and semi-Fredholm operators are also considered. The results obtained in this paper extend and improve many results in this area.     

从混合范数空间到Bloch型空间的加权微分复合算子（英文）

The boundedness and compactness of the weighted differentiation composition operators from mixed-norm spaces to Bloch-type spaces are discussed in this paper.     

Matching Realization of Uq（sln＋1） of Higher Rank in the Quantum Weyl Algebra Wq（2n）

In the paper, we further realize the higher rank quantized universal enveloping algebra Uq（sln＋1） as certain quantum differential operators in the quantum Weyl algebra Wq （2n） defined over the quantum divided power algebra Sq（n） of rank n. We give the quantum differential operators realization for both the simple root vectors and the non-simple root vectors of Uq（sln＋1）. The nice behavior of the quantum root vectors formulas under the action of the Lusztig symmetries once again indicates that our realization model is naturally matched.     

Approximation Theorems of Bernstein-Durrmeyer Operators in L_M~（Ba） Spaces

With the weighted modulus of smoothness as a metric,we prove the direct and the inverse theorems of approximation by Bernstein-Durrmeyer operators in LBa M spaces. Especially an approximation equivalent theorem of the operators is also obtained.     

一类q-Szsz-Mirakyan-Baskakov算子的逼近性质（英文）

In this paper we propose the q analogues of modified Baskakov-Sz′asz operators.we estimate the moments and establish the direct results in term of modulus of continuity.An estimate for the rate of convergence and weighted approximation properties of the q operators are also obtained.     

DENSENESS OF RADIAL-BASIS FUNCTIONS IN L^2（R^n） AND ITS APPLICATIONS IN NEURAL NETWORKS

The authors discuss problems of approximation to functions in L2(Rn) and operators fromL2(Rn1) to L2(Rn2) by Radial-Basis Functions. The results obtained solve the problem ofcapability of RBF neural networks, a basic problem in neural networks.     

算子的拟相似与(Q)类算子

本文引进定义于L(H)上的集值函数β(S)和(Q)类算子(指本质谱含于其一切拟相似算子的本质谱的算子),用β(S)刻划 (Q)类算子的特征;证明(Q)类算子范围广泛,次可分解算子(包括次标量算子,M-亚正常算子,半亚正常算子等等)是其中的一部分;(Q)类算子在L(H)中稠密.     

H~2(S)上Toeplitz算子本质谱的局部分解

本文利用Ｂａｎａｃｈ代数中局部化原理给出了多复变Ｈａｒｄｙ空间上Ｔｏｅｐｌｉｔｚ算子是Ｆｒｅｄｈｏｌｍ算子的一个充分必要条件；同时给出了Ｔｏｅｐｌｉｔｚ算子本质谱的局部分解．     

(NCI)算子与(NFI)算子

引入两类与不变子空间密切相关的算子,即(NCI)算子与(NFI)算子.考虑这两类算子的性质,例如存在性,相似不变性,以及与强不可约算子的关系等.并在可分Banach空间上讨论谱为单点集{0}的算子能否小紧摄动成为(NFI)算子.     

BANACH空间有界线性算子A~((2))_(T,S)的表示

In this paper we extends the results in [1],[2],[3] and [4] to bounded linear operators in Banach spaces using matrix expression of a partitioned operator. For existence of the limit lim λ→0 (λI + GA)~(-1) G and lim λ→0 G(λI + AG)~(-1) it is necessary and sufficient condition that bounded linear operators A~((2))_(T,S) exist in Banach spaces. We get the integral representation: A(2)_(T,S)=∫∞0 exp(-GAt)Gdt.     

扭化的Atiyah-Singer算子(I)

本文证明黎曼流表上的ｄｅ Ｒｈａｍ以及Ｓｉｇｎａｔｕｒｅ算子都同构于扭化的Ａｔｉｙａｈ－Ｓｉｎｇｅｒ算子。这两类算子的局部指数定理和局部Ｌｅｆｓｃｈｅｔｚ不动点公式都可以从扭化的Ａｔｉｙａｈ－Ｓｉｎｇｅｒ算子得到。     

Operators (not) similar to a contraction: Pisier's counterexample via singular integrals

The main difference of this exposition of Pisier's counterexample from the original one is that in the proof of the key inequality probabilistic considerations (like Brownian motion) are replaced by certain standard constructions from the theory of Calderòn-Zygmund operators. Bibliography: 9 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 79–95. Translated by S. V. Kislyakov.     

关于(s,p)-w-亚正常算子类

本文在W-亚正常算子类的基础上，引入（s，p）-w-亚正常算子类，进而讨论了该类算子的特征，包含关系，对一类特殊的该类算子还考虑了其平方性质．     

Dunford's property (C) and Weyl's theorems

This paper studies Weyl's theorems, and some related results for operators with Dunford's property (C). Weyl's theorem in some classes of operators (e.g.M-hyponormal,p-hyponormal and totally paranormal operators) is considered.     

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.     

THE STRUCTURE OF $\[\Pi \]$ SPACES (I)

The spectral theory of selfadjoint operators and unitary operators in Hilbert space has been successfully generalized to $\[{\Pi _k}\]$ space. However, there are only a few results for the spectral theory of selfadjoint operators and unitary operators in $\[\Pi \]$ space. One of the important reasons is that the structure of $\[\Pi \]$ space is more complex than that of $\[{\Pi _k}\]$ space. This paper and the forthcoming paper "The structure of $\[\Pi \]$ space (II)" will mainly be dealt with the structure of $\[\Pi \]$ spaces, which will be used to further study the operators in $\[\Pi \]$ spaces.