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Research of operator inequality and spectrum using computer

算子不等式与谱的计算机研究

基本信息

批准号：
14540190
负责人：
CHO Muneo
金额：
$ 2.11万
依托单位：
Kanagawa University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540190/
关键词：
Hilbert space trace formula principal function operator inequality Shannon inequality hyponormal operator Aluthge transform polar decomposition operator joint spectrum hyponormal n-tuple trace

项目摘要

Under the research project with title "Research of operator inequality and spectrum using computer", Takayuki Furuta (emerutus professor of Hirosaki University), Tadasi Huruya (Professor of Niigata University), Takeaki Yamazaki (Kanagawa University) and Muneo Cho (Kanagawa University) studied for three years. In this period, we invited V.Muller (Professor of Czech Academy), Andrzej Soltysiak (Professor of Adam Mickiewicz University), Woo Young Lee (Professor of Seoul University), Il Bong Jung (Professor of Kyungpook National University) and E.Albrecht (Professor of Universitat des Saarlandes) and studied this problem with them. Cho and Huruya studied principal functions started by M.Krein and studied continuously by J.Helton, R.Howe, R.Carey, J.Pincus, D.Xia and M.Putinar, who studied it in case of hyponormal operators and semi-hyponormal operators. We extended it in case of p-hyponormal operators and showed that the principal function of the Aluthge transformation is same the original one. We made 23 papers about these results. These have been published or will be published, recently. Furuta studied operator inequalities and got characterizations of chaotic order and generalized Kantorovich constant. He also applied these to Information Theory. He wrote 16 papers about these results. These have been published or will be published, recently. Yamazaki studied spectrum of operators. He got a spectrum-invariant transformation from class A to hyponormal operators. Also he studied numerical ranges by Aluthge transformation. He wrote 10 papers about these results. These have been published or will be published, recently. By this support, we wrote 49 papers. We express our cordial thanks for this Grant.

在题为“利用计算机研究算子不等式和谱”的研究项目下，古田隆之（广崎大学名誉教授）、呼谷忠司（新泻大学教授）、山崎武昭（神奈川大学）和赵宗雄（神奈川大学）进行了为期三年的研究。在此期间，我们邀请了V.Muller（捷克科学院教授）、Andrzej Soltysiak（亚当密茨凯维奇大学教授）、Woo Young Lee（首尔大学教授）、Il Bong Jung（庆北国立大学教授）和E.Albrecht（萨尔兰德斯大学教授），与他们一起研究这个问题。Cho和Huruya从M.Krein开始研究主函数，J.Helton，R.Howe，R.Carey，J.Pincus，D.Xia和M.Putinar继续研究，他们研究了亚正规算子和半亚正规算子的情况。我们将其推广到p-亚正规算子的情形，并证明了变换的主函数与原主函数相同。我们对这些结果发表了23篇论文。最近已经出版或即将出版。Furuta研究了算子不等式，得到了混沌序和广义Kantorovich常数的刻画.他还将这些应用于信息理论。他写了16篇关于这些结果的论文。最近已经出版或即将出版。山崎研究了算子谱。他得到了从A类到亚正规算子的谱不变变换。此外，他研究了数值范围内的变换。他写了10篇关于这些结果的论文。最近已经出版或即将出版。在此基础上，共撰写论文49篇。我们对这笔赠款表示衷心的感谢。