多个算子情形的Kadison不等式

假设φ是一个从有单位元的C~*代数到Hilbert空间上全体有界线性算子构成的代数B(H)上的保单位的正线性映射,经典的Kadison不等式是指对每个自伴元素A有φ(A)~2≤φ(A~2),该文利用Furuta不等式把这一不等式推广至多个算子情形.     

一些蕴含Furuta不等式的算子单调函数的算子不等式

本文研究了算子不等式与算子单调函数之间的联系.利用关于算子单调函数的乘积引理,乘积定理等基本控制原理,给出许多算子不等式,这些不等式可包含正算子理论中应有十分广泛的Furuta不等式.     

Jacobi算子的Hardy不等式及其应用

该文主要考虑与Jacobi算子相关的Hardy不等式.主要结果之一是求得了相关不等式的最佳常数.作为该不等式的应用之一,该文证明了,不同于欧式空间情形,双曲空间上的Hardy不等式可以整体的增添Brezis—Vazquez型余项.     

算子Dunkl-Williams型不等式

在于讨论和经典Dunkl-Williams型不等式相类似的算子不等式,得到了几个算子Dunkl-Williams型不等式,并将其与现有的不等式进行了比较,结果表明,所得的结果是前期结果的推广和改进.     

黎曼流形上散度型算子的低阶特征值估计(英文)

本文研究黎曼流形上散度型算子的低阶特征值.利用Rayleigh-Ritz不等式,得到了这种算子的低阶特征值所满足的一个不等式.而且,对于拉普拉斯算子的低阶特征值,本文的结果是最佳的.     

一些蕴含Furuta不等式的算子单调函数的算子不等式（英文）

本文研究了算子不等式与算子单调函数之间的联系.利用关于算子单调函数的乘积引理,乘积定理等基本控制原理,给出许多算子不等式,这些不等式可包含正算子理论中应有十分广泛的Furuta不等式.     

Hlder不等式和Minkowski不等式的推广

本文利用变分方法对多个变元的不含变元导数的Holder不等式和Minkowski不等式进行了推广．此种方法的主要意义不在于证明传统的不等式，而在于发现新的不等式．     

关于两个新型Hilbert不等式的推广

众所周知,Hilbert不等式是一个有重要应用的不等式,1998年,B．G．Pachpatte给出了类似Hilbert级数不等式的两个新不等式,本文的主要工作是推广了这两个新个新不等式。     

Hlder不等式和Minkowski不等式的推广

本文利用变分方法对多个变元的不含变元导数的H■lder不等式和Minkowski不等式进行了推广．此种方法的主要意义不在于证明传统的不等式,而在于发现新的不等式．     

关于几个新不等式

本文利用Redheffer不等式,Jordan不等式和Jensen不等式给出了一些新的不等式作为应用推广了文[1]的一个结果。     

An order preserving inequality for three operators via furuta inequality

Furuta showed that if A≥B≥0,then for each r≥0,f（p）=（A^r/2 B^p A^r/2）^t＋r/p＋r is decreasing for p≥t≥0.Using this result,the following inequality（C^r/2（AB^2A）^δC^ r/2）^ p-1＋r/4δ＋r ≤C^p-1＋r is obtained for 0〈p ≤1,r≥1,1/4≤δ≤1 and three positive operators A, B, C satisfy（A^1/2BA^1/2）^p/2≤A^p,（B^1/2AB^1/2）^p/2≥B^p,（C^1/2AC^1/2）^p/2≤C^p,（A^1/2CA^1/2）^p/2≥A^p.     

On Variance and Covariance for Bounded Linear Operators

In this paper we initiate a study of covariance and variance for two operators on a Hilbert space, proving that the c-v (covariance-variance) inequality holds, which is equivalent to the Cauchy-Schwarz inequality. As for applications of the c-v inequality we prove uniformly the Bernstein-type inequalities and equalities, and show the generalized Heinz-Kato-Furuta-type inequalities and equalities, from which a generalization and sharpening of Reid's inequality is obtained. We show that every operator can be expressed as a p-hyponormal-type, and a hyponormal-type operator. Finally, some new characterizations of the Furuta inequality are given. Received April 9, 2000, Revised July 20, 2000, Accepted August 8, 2000     

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．     

一个算子迹的不等式

本文讨论Bellman不等式的相关问题,利用紧算子的极表示以及陈公宁的一个矩阵迹的不等式,得到算子迹的相应不等式.作为其推论,在无穷维Hilbert空间中给出了Bellman问题的一个肯定回答.     

Generalized Aluthge transformation on -hyponormal operators

We shall introduce a generalized Aluthge transformation on -
hyponormal operators and also, by using the Furuta inequality, we shall give several properties on this generalized Aluthge transformation as further extensions of some results of Aluthge.

     

On the Bohr inequality of operators

This paper is focused on the operator inequalities of the Bohr type. We will give a new and transparent proof for the operator Bohr inequality through an absolute value operator identity, show some related operator inequalities by means of 2×2 (block) operator matrices, and finally we will present a generalization of the operator Bohr inequality for multiple operators.     

Numerous refinements of Pólya and Heinz operator inequalities

In this article, we present an infinite number of refinements of the Heinz inequality for real numbers and operators. Making use of them, infinitely many refinements of the classical Pólya inequality and their operator versions are deduced.     

Strict inequality of Robin eigenvalues for elliptic differential operators on Lipschitz domains

On a bounded Lipschitz domain we consider two selfadjoint operator realizations of the same second order elliptic differential expression subject to Robin boundary conditions, where the coefficients in the boundary conditions are functions. We prove that inequality between these functions on the boundary implies strict inequality between the eigenvalues of the two operators, provided that the inequality of the functions in the boundary conditions is strict on an arbitrarily small nonempty, open set.     

A Cotlar type inequality for the multilinear singular integral operators and its applications

A Cotlar type inequality is established for the multilinear singular integral operators. As applications, some two-weight norm inequalities are obtained for the maximal operator corresponding to the multilinear singular integral operators.     

Existence of solutions for hyperbolic hemivariational inequalities

In this paper we study a hyperbolic hemivariational inequality with a nonlinear, pseudomonotone operator depending on the derivative of an unknown function and a linear, monotone operator depending on an unknown function. Using the surjectivity result for L-pseudomonotone operators, an existence result for such inequalities is proved.