王云,闫成

• 1:新疆大学数学与系统科学学院

摘要(Abstract)：

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)~((p)~+)使得x_iy_i=y_ix_i,i=1,2,…,n,我们证明了‖(∑_(j=1)~kx_i~(1/2)y_i~(1/2))~2‖_(E(M)~((r)))≤‖(∑_(j=1)~kx_i)~(1/2)(∑_(j=1)~ky_i)(∑_(j=1)~kx_i)~(1/2)‖_(E(M)~((r)))≤‖(∑_(j=1)~kx_i)(∑_(j=1)~ky_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.

关键词(KeyWords)： log-次优化不等式;von Neumann代数;非交换对称拟Banach空间

Abstract:

Keywords:

基金项目(Foundation): 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)~~

作者(Author): 王云,闫成

DOI: 10.13568/j.cnki.651094.651316.2020.06.06.0002

参考文献(References)：

• [1]BOURIN J C.Matrix subadditivity inequalities and block-matrices[J].International Journal of Mathematics,2009,20(1):679-691.
• [2]HAYAJNEH S,KITTANEH F.Trace inequalities and a question of bourin[J].Bulletin of the Australian Mathematical Society,2013,88(3):384-389.
• [3]LIN M.Remarks on two recent results of Audenaert[J].Linear Algebra and its Applications,2016,489(1):24-29.
• [4]LIU J,WANG Q,SUN F.On Hayajneh and Kittaneh’s conjucture on unitarily invariant norm[J].Journal of Mathematical Inequalities,2017,11(4):1019-1022.
• [5]HAN Y Z,SHAO J J.Notes on two recent results of Audenaert[J].Electronic Journal of Linear Algebra,2016,31(1):147-155.
• [6]DODDS P G,DODDS T K,SUKOCHEV F A.On p-convexity and q-concavity in noncommutative symmetric spaces[J].Integral Equations and Operator Theory,2014,78(1):91-114.
• [7]FACK T,KOSAKI H.Generalized s-numbers ofτ-measurable operators[J].Pacific Journal of Mathematics,1986,123(2):269-300.
• [8]韩亚洲,吐尔德别克.非交换Lp(M;τ)空间中有关连加和及直和的一些不等式[J].新疆大学学报(自然科学版),2009,26(4):408-418.HAN Y Z,BEKJAN T N.Some Inequalities for sums and direct sums of noncommutative spaces operators[J].Journal of Xinjiang University(Natural Science Edition),2009,26(4):408-418.(in Chinese)
• [9]FACK T.Sur la notion de valeur caracteristique[J].Journal of Operator Theory,1982,7(2):307-333.
• [10]BEKJAN T N.Noncommutative symmetric Hardy spaces[J].Integral Equations and Operator Theory,2015,81(2):191-212.
• [11]MOSLEHIAN M S,KIAN M,XU Q H.Positivity of 2×2 block matrices of operators[J].Banach Journal of Mathematical Analysis,2019,13(3):726-743.
• [12]KOSAKI H.An inequality of Araki-Lieb-Thirring(Von Neumann Algebra case)[J].Proceedings of the American Mathematical Society,1992,114(2):477-481.
• [13]HAN Y Z.Submajorization and p-norm inequalities associated with measurable operators[J].Linear and Multilinear Algebra,2017,65(11):2199-2211.
• [14]BEKJAN T N,OSPANOV M N.H¨older-type inequalities of measurable operators[J].Positivity,2017,21(1):113-126.
• [15]DODDS P G,DODDS T K,SUKOCHEV F A,et al.Logarithmic submajorization,majorization and H¨older type inequalities forτ-measurable operators[EB/OL].Indagationes Math,doi:10.1016/j.indag.2020.02.004.
• [16]XU Q H.Analytic functions with values in lattices and symmetric spaces of measurable operators[J].Mathematical Proceedings of the Cambridge Philosophical Society,1991,109(3):541-563.
• [17]DODDS P G,DODDS T K.On a submajorization inequality of T Ando[J].Operator Theory:Advances and Application,1995,75(1):113-131.
• [18]CHONG K M.Some extensions of a theorem of Hardy,Littlewood and P′olya and their applications[J].Canadian Journal of Mathematics,1974,26(6):1321-1340.
• [19]DODDS P G,SUKOCHEV F A.Submajorization inequalities for convex and concave functions of sums of measurable operators[J].Positivity,2009,13(1):107-124.
• [20]BEKJAN T N,MASSEN G.Submajorization of the Araki-Lieb-Thirring inequality[J].Kyushu Journal of Mathematics,2015,69(1):387-392.