Research of operator inequality and spectrum using computer

在题为“利用计算机研究算子不等式和频谱”的研究项目中，古田孝之（hiroaki大学名誉教授）、新泻大学教授胡屋忠西（Tadasi Huruya）、山崎武明（神奈川大学）和Cho Muneo（神奈川大学）进行了三年的研究。在此期间，我们邀请了捷克科学院教授V.Muller、Adam Mickiewicz大学教授Andrzej Soltysiak、首尔大学教授Woo Young Lee、庆北大学教授Il Bong Jung、Saarlandes大学教授E.Albrecht一起研究了这个问题。Cho和Huruya研究了由M.Krein开始的主函数，J.Helton、R.Howe、R.Carey、J.Pincus、D.Xia和M.Putinar继续研究了它们在次正规算子和半次正规算子情况下的主函数。对p-次正规算子进行了推广，证明了Aluthge变换的主函数与原主函数相同。我们就这些结果发表了23篇论文。这些都是最近已经出版或即将出版的。Furuta研究了算子不等式，得到了混沌序和广义Kantorovich常数的刻画。他还将这些理论应用于信息论。他写了16篇关于这些结果的论文。这些都是最近已经出版或即将出版的。Yamazaki研究了算子的频谱。他得到了从a类算子到次正规算子的谱不变变换。并用Aluthge变换研究了数值范围。他就这些结果写了10篇论文。这些都是最近已经出版或即将出版的。在这种支持下，我们写了49篇论文。我们对这笔赠款表示衷心的感谢。

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.