Operator-Theoretic Methods for Matrix Inequalities

矩阵不等式的算子理论方法

• 批准号: 08640230
• 负责人: ANDO Tsuyoshi
• 金额: $ 1.41万
• 依托单位: Hokusei Gakuen University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08640230/
• 关键词: matrix inequality; eignvalue inequality; norm inequality; Holder type inequality; Hadamard product; majorization; 作用素半径; ノルム評価; 擬順序

1 The Golden-thompson inequality concerning exponential functions for a pair of matrices is generalized to the case of more than three matrices by using Hadamard products.[Reference 1]2 Performing inverse operations before and after a positive linear map produces stronger order relation. The fundamental structure of this strong order is analyzed.[Reference 2]3 A reasonable upper bound is given for the farthest distance from one normal matrix to the set of unitary orbits of the other normal matrix.[Reference 3]4 Besides the usual norms, a family of operator radii omega_<rho>(・)(0<rho<*) is considered in the space of matrices. An interpolation theorem, in the form of Holder type inequality, is established for this family of operator radii with respect to Hadamard multiplication. [Reference 4, 5]5 A way of generalizing the Holder type inequality to the matrix case is investigated. They are established in the form of matrix inequality as well as in the trace inequality. [Reference 6]A survey article with title Operator-Theoretic Methods for Matrix Inequalities is prepared to let the results widely be recognized by researchers in the world.

1通过使用Hadamard产品，将有关一对物质的指数函数的黄金 - 敦促不平等概括为三个以上的物质。[参考文献1] 2在正线性图之前和之后进行逆操作会产生更强的订单关系。分析了这种强度的基本结构。[参考2] 3从一个正常矩阵到另一个正常矩阵的一组单一轨道的最远距离，给出了合理的上限。[参考3] 4除了通常的规范外，一个常规规范，一个经营者Radii Omega__ <rho>（0 <rho <rho <rho <*）的经营者radii omega__ <rho>（0 <rho <*）。以持有人类型不平等的形式进行插值理论，是针对Hadamard乘法的该家族的Radii家族建立的。 [参考4，5] 5研究了一种将持有人类型不等式推广到矩阵案例的方法。它们是以基质不平等以及痕量不平等的形式建立的。 [参考文献6]一份带有标题操作员理论方法的调查文章已准备好使结果被世界研究人员广泛认可。

项目成果

T.Ando: "Bounds for anti-distance" Journal of Convex Analysis. 3-3. 371-373 (1996)

T.Ando：“反距离的界限”凸分析杂志。

T.Ando and K.Okubo: "Holder-type inequalities associated with operator radii and Schur products" Linear and Multilinear Algebra. 43-1. 53-61 (1997)

T.Ando 和 K.Okubo：“与算子半径和 Schur 产品相关的保持器类型不等式”线性和多重线性代数。

T.Ando: "Bounds for anti-distance" Journal of Convex Analysis. 3・3. 371-373 (1996)

T.Ando：“反距离的界限”凸分析杂志 3・3（1996）。

T.Ando and F.Hiai: "Holder type inequalities for matrices" Mathematical Inequalities & Applications. 1・1. 1-30 (1998)

T.Ando 和 F.Hiai：“矩阵的持有人型不等式”数学不等式和应用 1・1（1998）。

T.Ando and F.Hiai: "Holder-type inequalities for matrices" Mathematical Inequalities & Applications. 1-1. 1-30 (1998)

T.Ando 和 F.Hiai：“矩阵的 Holder 型不等式” 数学不等式