Research of operator inequality and spectrum using computer

在题为《用计算机研究算子不等式和谱》的研究项目下，古田隆之(Hirosaki University)教授Takayuki Furuta、新泻大学教授Tadasi Huruya、神奈川大学(Kanagawa University)山崎武明(Takeaki Yamazaki)和神奈川大学(Muneo Cho)研究了三年。在此期间，我们邀请了V.Muller(捷克学院教授)、Andrzej Soltysiak(Adam Mickiewicz大学教授)、Woo Young Lee(首尔大学教授)、Il Bong Jung(京布国立大学教授)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研究了M.Krein开始的主函数，J.Helton，R.Howe，R.Carey，J.Pincus，D.Xia和M.Putina继续研究了主函数，他们在亚正规算子和半正规算子的情况下研究了它。我们将其推广到p-次正规算子的情形，证明了Aluthge变换的主函数与原变换的主函数相同。我们就这些结果发表了23篇论文。这些书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论。他就这些结果写了16篇论文。这些书最近已经出版或即将出版。山崎研究了算符的谱。他得到了从A类到次正规算子的谱不变变换。他还用Aluthge变换研究了数值值域。他就这些结果写了10篇论文。这些书最近已经出版或即将出版。在这一支持下，我们写了49篇论文。我们对这笔赠款表示诚挚的感谢。

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.