2×2分块算子矩阵单值扩张性

结合有界线性算子单值扩张性的相关结论,研究了上三角分块算子矩阵■的单值扩张性,与此同时,通过扰动理论讨论了2×2分块算子矩阵■的单值扩张性,得到了M_C与M有单值扩张性的充要条件.进一步,对无穷维Hamilton算子H得到了H与H*的单值扩张性等价的结论.最后,对上三角无穷维Hamilton算子■得到了H与对角元的单值扩张性等价的结论.     

误差估计中矩阵求逆条件数的最优性在Hilbert空间中的推广

本文利用Hilbert空间中可逆算子的极发解定理，将误差估计中矩阵求逆条件数的最优性在Hilbert空间中进行推广，证明了线性有界算子A的求逆条件数K(A)=‖A‖A^-1‖在求算子扰动逆(A E)^-1的相对误差界中的极小性质，指出了算子求逆条件数在误差估计为仅与算子A有关的最佳常数值。     

有界线性算子逼近问题中算子本质谱弧立点的处理

在Hilbert空间线性算子逼近论中,算子本质的孤立点通常是处理一些问题的主要障碍之一,本给出处理算子本质谱的孤立点的一般方法。     

Γ-inverses of Bounded Linear Operators

Let B(H) be the algebra of all the bounded linear operators on a Hilbert space H.For A,P and Q in B(H),if there exists an operator X∈ B(H) such thatAP X QA=A,X QAP X=X,(QAP X)*=QAP X and(X QAP)*=X QAP,then X is said to be the Γ-inverse of A associated with P and Q,and denoted by AP,Q+.In this note,we present some necessary and su?cient conditions for which A+P,Qexists,and give an explicit representation of AP,Q+(if AP,Q+exists).     

一类单胞加权移位算子

设H是复的可分Hilbert空间，｛am｝∞^m=0是由正实数组成的有界数列，对于H上的内射有界线性算子A，以及f(≠0）∈H，我们令ωm=αm||A^m 1f||/||A^mf|| m=0,1,2,…。设Tω是H以上｛am｝m^∞=0为权序列的单边加权移位算子。本文讨论了Tω的单胞性，其主要结果推广了B.S.Yadav和S.Chatterjee的工作[4]。     

Operator Matrix Forms of Positive Operators

If a 3-tuple (A:H1→H1,B:H2→H1,C:H2→H2）of operators on Hibert spaces is given,we proved that the operator ～↑A:=(↑A ↓B^*↑B ↓C) on H=H1 H2 is ≥0 is and only if A≥0,R(B)∪→R（A^1/2) and C≥B^* A^ b,where A^ is the generalized inverse of A.In general,A^ is a closed operator,but since R(B)∪→R(A^1/2,B^* A^ B is bounded yet.     

On p-ω-hyponormal Operators

In this paper, we show that if T is p-ω-hyponormal, the nonzero points of the approximate and joint approximate point spectrum of T are identical; Moreover, we obtain a pair of inequalities similar to p-ω-hyponormal operators.     

Commuting Toeplitz Operators with Harmonic Symbols on A2（D,dμ）

For any given symmetric measure μ on the closed unit disk D, we apply the Berezin transform to characterizing semi-commuting and commuting Toeplitz operators with bounded harmonic symbols on A2（D, dμ）.     

Boundedness of Multilinear Caldern–Zygmund Singular Operators on Morrey–Herz Spaces with Variable Exponents

In this paper,we introduce Morrey–Herz spaces M K˙(·)q,p(·)(Rn) with variable exponents α(·) and p(·),and prove the boundedness of multilinear Caldern–Zygmund singular operators on the product of these spaces.     

Hilbert空间上线性算子广义逆A_(T,S)~((2))的存在性及其表示式

设H1和H2是两个Hilbert空间,B(H1,H2)表示从H1到H2的所有有界线性算子的集合,T和S分别是H1和H2的两个闭子空间．如果存在线性算子X∈B(H2,H1)满足XAX=X,R(X)=T,N(X)=S,则称X为线性算子A的具有指定像空间T和零空间S的外逆,记为AT,S(2)．该文进一步研究了线性算子广义逆AT,S(2)存在的若干等价条件及其性质,建立了算子广义逆AT,S(2)的表示形式．     

METRIC GENERALIZED INVERSE OF LINEAR OPERATOR IN BANACH SPACE＊＊＊

The Moore-Penrose metric generalized inverse T of linear operator T in Banach space is systematically investigated in this paper. Unlike the case in Hilbert space, even T is a linear operator in Banach Space, the Moore-Penrose metric generalized inverse T is usually homogeneous and nonlinear in general. By means of the methods of geometry of Banach Space, the necessary and sufficient conditions for existence, continuitv, linearity and minimum property of the Moore-Penrose metric generalized inverse T will be given, and some properties of T will be investigated in this paper.     

Regularity of Continuous Linear Operators on Banach Function Spaces

In this paper we present some characterizations of Banach function spaces on which every continuous linear operator is regular.     

On Bounds for Spectra of Operator Pencils in a Hilbert Space

A class of pencils(operator-valued functions of a complex argument) in a separeble Hilbert space is considered.Bounds for the spectra are derived.Applications to differential operators,integral operators with delay and in finite matrix pencils are discussed.     

Lipschitz映射的一些局部性质

本文直接从F~+(x,y~(?),h)出发,研究了Banach空间上Lipsohitz映射一些局部性质的判断条件,得到了A.D.Ioffe在文[1]中的类似结果,且证明比较简单明了。     

Lipschitz映射的一些局部性质

本文直接从 F~+(x;y,h)出发,研究了 Banach 空间上 Lipschitz 映射一些局部性质的判断条件,得到了 A.D.Ioffe 在文[1]中的类似结果,且证明比较简单明了.     

CBMO estimates for multilinear Hardy operators

The purpose of this paper is to study the multilinear Hardy operators in higher dimensional cases and establish the CBMO estimates for multilinear Hardy operators on some function spaces, such as the Lebesgue spaces, the Herz spaces and the Morrey-Herz spaces.     

关于Moore-Penrose逆T+连续性的一个注

设X为拓扑空间.H1和H2为Hilbert空间,T(·)为X到B(H1,H2)的连续映射.本文主要利用Tikhonov正则化算子给出了Moore-Penrose逆T x连续的充分必要条件.这个结果在计算数学中是很重要的.     

一类具有离散谱的对称微分算子

研究了一类2n-阶线性微分算子在加权Hilbert空间中的谱.通过对加权Sobolev空间H     

APPROXIMATING SOLUTION OF 0∈ T（x） FOR AN H-MONOTONE OPERATOR IN HILBERT SPACES

The purpose of this paper is to study the solution of 0 ∈ T (x) for an H-monotone operator introduced in [Fang and Huang, Appl. Math. Comput. 145(2003)795-803] in Hilbert spaces, which is the first pro...