有关p-亚正规算子和对数亚正规算子广义Aluthge变换的一个注解

We shall give some results on generalized aluthge transformation for p-hyponormal and log-hyponormal operators.We shall also discuss the best possibility of these results.     

关于拉普拉斯谱半径的一个不等式

设G是一个简单连通图,v是图G的一个割点.G_1,G_2,…,G_s(s≥2)是图G的s个v-分支.令H_1=G_1∪G_2∪…∪G_t,H_2=G_(t+1)∪G_(t+2)∪…∪G_s,其中1≤t相似文献   

Some graft transformations and its applications on the distance spectral radius of a graph

Let D(G)=(d_i,j)_n×n denote the distance matrix of a connected graph G with order n, where d_ij is equal to the distance between v_i and v_j in G. The largest eigenvalue of D(G) is called the distance spectral radius of graph G, denoted by ?(G). In this paper, some graft transformations that decrease or increase ?(G) are given. With them, for the graphs with both order n and k pendant vertices, the extremal graphs with the minimum distance spectral radius are completely characterized; the extremal graph with the maximum distance spectral radius is shown to be a dumbbell graph (obtained by attaching some pendant edges to each pendant vertex of a path respectively) when 2≤k≤n−2; for k=1,2,3,n−1, the extremal graphs with the maximum distance spectral radius are completely characterized.     

Some graft transformations and its application on a distance spectrum

Let D(G)=(d_i,j)_n×n denote the distance matrix of a connected graph G with order n, where d_ij is equal to the distance between v_i and v_j in G. The largest eigenvalue of D(G) is called the distance spectral radius of graph G, denoted by ?(G). In this paper, we give some graft transformations that decrease and increase ?(G) and prove that the graph (obtained from the star S_n on n (n is not equal to 4, 5) vertices by adding an edge connecting two pendent vertices) has minimal distance spectral radius among unicyclic graphs on n vertices; while (obtained from a triangle K₃ by attaching pendent path P_n−3 to one of its vertices) has maximal distance spectral radius among unicyclic graphs on n vertices.     

关于wF(p,r,q)算子类

作为wA(p,r)算子类的一个推广,该文介绍了一类更广泛的算子类即 wF(p,r,q)算子类,它包含A(p,r)类而含于F(p,r,q)类之中, 进而考虑了该类算子的特征, 包含关系, 正规性和幂性质等等.     

On Young and Heinz inequalities for τ-measurable operators

The purpose of this article is to prove Young and Heinz inequalities for τ-measurable operators.     

Improved Young and Heinz inequalities for matrices

We give refinements of the classical Young inequality for positive real numbers and we use these refinements to establish improved Young and Heinz inequalities for matrices.     

极分解与广义*-Aluthge变换

首先给出了Hilbert空间上有界线性算子极分解的的若干性质.其次指出广义的*-Aluthge变换与*-Aluthge变换具有许多相似性质;例如,T_(α,β)^((*))=U|T_(α,β)((*))=U|T_(α,β)^((*))|当且仅当T是双正规的,即[|T|,|T*|]=0,其中对任意两个算子A和B,[A,B]=AB-BA.     

矩阵的几个不等式

利用谱分解定理和几个标量不等式,得到了矩阵加权几何均值和酉不变范数的几个不等式,它们是Kittaneh和Manasrah所得相关结果的改进.     

具有固定直径的树的拉普拉斯谱半径

一个图称为毛毛虫,如果从它删去所有的悬挂点后得到的图是一个路.研究了具有固定直径的毛毛虫树的拉普拉斯谱半径,确定了其中具有最大拉普拉斯谱半径的毛毛虫树并且讨论了该树的一些性质.     

Heinz type inequalities for mappings satisfying Poisson’s equation

In this paper, we study the Heinz type inequalities for mappings satisfying Poisson’s equation. Some results generalize the ones obtained by Partyka and Sakan.     

变换图的正则性和谱半径

在前人对八种变换图研究的基础上,探讨了变换后满足正则性的原图的性质,得到了如下结果:G~( )及G~(---)是正则图当且仅当G是正则图;G~( -)和G~(-- )为正则图的充要条件是G为C_n、K_(2,n-2)或K_4;G~( - )和G~(- -)是正则图当且仅当G为C_5、K_7、K_2、K_(3,3)或G_0;G~(- )和G~( --)是正则的当且仅当G是(n-1)/2-正则图．同时还讨论了变换图的谱半径上界,并对这些上界进行了估计．     

p-ω-亚正规算子的一些性质

In this paper,let T be a bounded linear operator on a complex Hilbert H.We give and prove that every p-w-hyponormal operator has Bishop's property(β)and spectral properties;Quasi-similar p-w-hyponormal operators have equal spectra and equal essential spectra.Finally,for p-w-hyponormal operators,we give a kind of proof of its normality by use of properties of partial isometry.