有关算子的一些Log-次优化不等式和对称拟范数不等式  

Logarithmic Submajorization and Symmetric Quasi-Norm Inequalities on Operators

作　　者：王云 闫成[1] WANG Yun;YAN Cheng(School of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 830046,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《新疆大学学报（自然科学版）（中英文）》2021年第4期407-424,共18页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：天山青年计划-优秀科技人才项目(2018Q012);新疆维吾尔自治区自然科学基金(2018D01C073);国家自然科学基金(11761067).

摘　　要：本文利用优化理论及拟范数的性质研究了与Hayajneh-Kittaneh猜想相关的算子不等式.设E(M)是非交换对称拟Banach空间,x_(i)∈E(M)^((p)+),y_(i)∈E(M)^((q)+)使得x_(i)y_(i)=y_(i)x_(i),i=1,2,…,n,我们证明了||(∑^(k)_(j)=1 x^(1/2)^(i)y^(1/2)_(i))^(2)||E(M)^((r))≤(∑^(k)_(j)=1_(xi))^(1/2)(∑^(k)_(j)=1 y i)(∑^(k)_(j)=1 x i)^(1/2)||E(M)^((r))≤||(∑^(k)_(j)=1 x i)(∑^(k)_(j)=1 y i)||E(M)^((r)).其中1≤p,q,r<∞且1/r=1/p+1/q.同时我们还给出了一些与log-次优化相关的不等式.Using the method of majorization and the properties of quasi-norms,we give some quasi-norm inequalities related to Hayajneh and Kittaneh’s conjecture for operator in semifinite von Neumann algebras.Let E(M)be symmetric quasi-Banach spaceandlet x_(i)∈E(M)^((p)+),y_(i)∈E(M)^((q)+)with x_(i)y_(i)=y_(i)x_(i),i=1,2,…,n,then||(∑^(k)_(j)=1 x^(1/2)^(i)y^(1/2)_(i))^(2)||E(M)^((r))≤(∑^(k)_(j)=1_(xi))^(1/2)(∑^(k)_(j)=1 y i)(∑^(k)_(j)=1 x i)^(1/2)||E(M)^((r))≤||(∑^(k)_(j)=1 x i)(∑^(k)_(j)=1 y i)||E(M)^((r)).Some logarithmic submajorization inequalities for operator in semifinite von Neumann alge-bras are also considered.

关 键 词：log-次优化不等式 VONNEUMANN代数 非交换对称拟Banach空间 

分 类 号：O177.1[理学—数学]