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τ-可测算子迹的不等式
作者姓名:Mohammad Sal Moslehian  ;Ghadir Sadeghi
作者单位:[1]马什哈德菲尔多西大学理论数学系,马什哈德91775,伊朗; [2]哈基姆萨卜泽瓦尔大学数学与计算机科学系,萨卜泽瓦尔,伊朗
摘    要:设m是具有忠实正规半有限迹τ的Hilbert空间上的一个半有限von Neumann代数.隶属于m的—个闭稠定算子x称为τ可测,如果存在常数λ≥0使得τ(e|x|(λ,∞))〈∞.将一些很有用的已知的Hilbert空间算子迹的不等式推广到τ-可测算子迹.特别是这些不等式蕴涵了n-元τ-可测算子的Clarkson不等式.同时还给出了τ-可测算子的广义平行四边形法则.

关 键 词:半有限von  Neumann代数  τ-可测算子    Clarkson不等式

Inequalities for trace on τ-measurable operators
Mohammad Sal Moslehian,;Ghadir Sadeghi.Inequalities for trace on τ-measurable operators[J].Communication on Applied Mathematics and Computation,2014(4):379-389.
Authors:Mohammad Sal Moslehian  Ghadir Sadeghi  
Institution:Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures(CEAAS), Ferdowsi University of Mashhad, Mashhad 91775, Iran 2. Department of Mathematics and Computer Sciences, Hakim Sabzevari University Sabzevar, Iran)
Abstract:Let 971 be a semifinite von Neumann algebra on a Hilbert space equipped with a faithful normal semifinite trace r.A closed densely defined operator x affiliated with(?) is called τ-measurable if there exists a number λ≥0 such thatτ(e~|x|(λ,∞)) 〈∞.A number of useful inequalities,which are known for the trace on Hilbert space operators,are extended to trace on τ-measurable operators.In particular,these inequalities imply the Clarkson inequalities for n-tuples of τ-measurable operators.A general parallelogram law for τ-measurable operators are given as well.
Keywords:semifinite von Neumann algebra  τ-measurable operator  trace  Clarkson inequality
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