Study on operator inequalities based on various analytic methods

基于多种解析方法的算子不等式研究

• 批准号: 23540215
• 负责人: KOSAKI Hideki
• 金额: $ 3.16万
• 依托单位: Kyushu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23540215/
• 关键词: 作用素平均; 正定値関数; 量子情報理論; 完全正写像; Jensen型不等式; 作用素ノルム不等式; ノルム不等式

To get norm comparison results for operator means we have to check positive definiteness of ratios of relevant means. By computing Fourier transforms we have checked positive definiteness of a variety of ratios. We have also made use of the concept of infinite divisibility to establish this for some ratios whose explicit computations of Fourier transforms seem hopeless.On the other hand, our technique was proved useful for study on completely positive maps appearing naturally in quantum information theory.

为了得到算子均值的范数比较结果，我们必须检验相关均值比率的正定性。通过计算傅里叶变换，我们检验了各种比率的正定性。我们还利用无穷可除性的概念为某些比例建立了这一点，这些比例的傅里叶变换的显式计算似乎是不可能的。另一方面，我们的技术被证明对量子信息论中自然出现的完全正映射的研究是有用的。

项目成果

C*-algebras associated with complex dynamical systems and backward orbit structure

与复杂动力系统和后向轨道结构相关的 C* 代数

• 发表时间: 2014
• 期刊: Complex anal. Oper. Theory
• 作者: J. Pruss; 清水扇丈;Minoru Itoh;杉本 充;Yoshio Tsutsumi and Shuji Yoshikawa;梅田亨;清水扇丈;Yoshio Tsutsumi;杉本 充;S. Ino and Y. Watatani;清水扇丈;梅田亨;Mitsuru Sugimoto;Yoshio Tsutsumi;T. Kajiwara and Y. Watatani
• 通讯作者: T. Kajiwara and Y. Watatani

KMS STATES ON FINITE-GRAPH <i>C</i>^∗-ALGEBRAS

有限图上的 KMS 状态 <i>C</i>^*-代数

• DOI: 10.2206/kyushujm.67.83
• 发表时间: 2013
• 期刊: Kyushu Journal of Mathematics
• 影响因子: 0.4
• 作者: T. Kajiwara and Y. Watatani

Positive definiteness of functions with applications to operator norm inequalities

• 发表时间: 2011
• 作者: 幸崎 秀樹

Families of completely positive maps associated with monotone metrics

与单调度量相关的完全正映射族

• 发表时间: 2013
• 期刊: Linear Algebra Appl
• 影响因子: 1.1
• 作者: F.Hiai;H.Kosaki;D.Petz and M.B.Ruskai
• 通讯作者: D.Petz and M.B.Ruskai