We study the refinement of arithmetic-harmonic mean inequalities.First,through the classical analysis method,the scalar inequalities are obtained,and then extended to the operator cases.Specifically,we have the following main results:for 0 ＜ v,τ ＜ 1,a,b ＞ 0 with (b-a)(τ-v) ＞ 0,we have a▽vb-a!vb/a▽τb-a!τb ≤ τ(1-τ)/τ(1-τ) and (a▽vb)2-(a!vb)2/(a▽τb)2-(a!τb)2 ≤v(1-v)/τ(1-τ),which are generalizations of the results of W.Liao et al.

In this paper,we will define two transformations from class A to the class of hyponormal operators,which are n-th operators transformation (T)n of (T) and the n-th operators transformation (T)n(*) of(T)(*),and give their some properties.

In this paper, we study the relations between the operator inequalities and the operator monotone functions. By using the fundamental conclusions based on majorization, namely, product lemma and product theorem for operator monotone functions, we can give some operator inequalities. This result contains the Furuta inequality, which has a huge impact on positive operator theory.

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(A2),该文利用Furuta不等式把这一不等式推广至多个算子情形.

In this paper,firstly,we give some properties for the polar decomposition of a bounded linear operator.Secondly,we show that the generalized *-Aluthge transformation has some similar properties as *-Aluthge transformation;for example,T_(α,β)~((*)) = U|T_(α,β)~((*))| if and only if T is binormal,i.e.,[|T|,|T~*|]=0,where[A,B]= AB - BA for any operator A and B.

In this paper,we shall show an equivalence relation between extensions of order preserving operator inequalities and monotonicity of related Furuta type operator functions.

In this paper,the authors mainly give some properties of von Neumann-Jordan type constants.First,they characterize some equivalent conditions of uniformly non-square by von Neumann-Jordan constants.Second,they discuss the relation between von Neumann-Jordan type constant and normal structure.Finally,they give some relations among C_1′(X),C_1(X) and other constants.

As a generalization of grand Furuta inequality,recently Furuta obtain:If A≥ B≥0 with A0,then for t∈[0,1]and p1,p2,p3,p4≥1, A t 2[A- t 2{A t 2(A/ t 2 Bp 1A /t2 )p 2A t 2}p 3A -t2 ]p 4A t 2 1 [{(p1/t)p2+t}p3-t]p4+t]≤A. In this paper,we generalize this result for three operators as follow:If A≥B≥C≥0 with B0,t∈[0,1]and p1,p2,···,p2n/1,p2n≥1 for a natural number n.Then the following inequalities hold for r≥t, A1/t+r≥ [A r 2[B /t 2{B t 2······[B /t 2{B t 2(B /t 2 ←B /t 2 n times Bt 2 n/1 times by turns Cp 1B /t 2)p 2B t 2}p 3B /t 2]p 4···B t 2}p 2n/1B /t 2 B /t 2 n times Bt 2 n/1 times by turns→ ]p 2nA r 2] 1/t+r q[2n]+r/t, where q[2n]≡{···[{[(p1-t)p2+t]p3/t}p4+t]p5/···/t}p2n+t /t and t alternately n times appear .

In this article,we study the problem of Furuta-type operator inequality.By using the Lwner-Heinz inequality and an Uchiyama inequality,we extend an order preserving operator inequality from two operators to several operators,which is a generalization of Furuta's result.

Let X be a Banach space.We study the properties about the parameter H(a,X)=sup{‖x+y‖∧(a+1)x-y:x∈S(X),y,y-ax∈B(X),a≥0}.The main result is that a Banach space X with H(a,X)(3+a)/2 for some a∈ has uniform normal structure.

Let T∈B(H) be a bounded linear operator on a complex Hilbert space H.In this paper the authors introduce a new class of operator-quasi-*-A(n) and prove some properties of these operators,such as,if T is quasi-*-A(n),then its point spectrum and joint point spectrum are identical.Using these results,the authors also prove that if T or T* is quasi-*-A(n),then the spectral mapping theorem holds for the weyl spectrum and for the essential approximate point spectrum.

The purpose of this paper is to study the strong convengence of a general iterative process to find a common element of the set of fixed points of nonexpansive mapppings and the set of solutions of variations inequality for a strongly monotone mapping.

<正>Banach空间几何是泛函分析理论中的重要部分,近几年来Banach空间上的几何常数是数学工作者研究的热点内容之一.在文献[1]中作者根据几何平均在Banach空间上引入了两个几何常数.本文根据两个正数的调和平均即M(a,b)=(1/a)+2(1/b)=a2+abb,其中a,b是两个正实数,定义了一类新的几何常数H(X)

This paper,according to Gao′s constant,introduces the generalized Gao′s constant,and give some simple properties about the constant.Additionally,some sufficient conditions for uniform normal structure of a Banach space are given,and the results can be seen as a further promotion of the original ones.

In this paper,under the framework of a strictly convex Banach space with a uniformly Gteaux differentiable norm,we study strong convergence of two explicit viscosity approximation methods for finding a solution to the variational inequality with weakly contractive mapping A,and give the estimate of convergence rate.

In this paper,we give some sufficient conditions for the(DL)-condition in terms of generalized James constant,generalized Jordan-von Neumann constant,and the coeffcient of weak orthogonality.A a consquence,we obtain fixed point theorems for theorems for multivalued nonexpansive mappings.

This paper gives some properties of the generalized James constant J(t,X),at the same time it also shows that if t1,J(t,X)t+t2+42,then Banach spaces X have uniform normal structure.

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.

设C是复数域, H是C上无穷维可分的 Hibert 空间,B(H)及K(H) 分别表示H上有界线性算子和紧算子的全体.若T∈B(H),记σ(T),σa(T),σea(T)及σja(T) 分别表示T的谱, 近似点谱,本质近似点谱及联合近似点谱[1,2].

By systematical research on local spectral theory of class wF(p,r,q) operators,a series of results have been obtained:such as class wF(p,r,q) operators is subscalar operator,class wF(p,r,q) operators is subdecomposable,the local spectral subspace of class wF(p,r,q) operators is equal to the maximal algebraic spectral subspace of class wF(p,r,q) operators,class wF(p,r,q) operators has finite ascent,and so on.