2004 Fiscal Year Final Research Report Summary
Research of operator inequality and spectrum using computer
| Project/Area Number |
14540190
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kanagawa University |
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Principal Investigator |
CHO Muneo Kanagawa University, Faculty of Engineering, 工学部, 教授 (10091620)
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| Co-Investigator(Kenkyū-buntansha) |
FURUTA Takayuki Hirosaki University, Emerutus Professor, 名誉教授 (40007612)
HURUYA Tadasi Niigata University, Faculty of Education and Human Science, 教育人間科学部, 教授 (90018648)
YAMAZAKI Takeaki Kanagawa University, Faculty of Engineering, 工学部, 講師 (60333150)
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| Project Period (FY) |
2002 – 2004
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| Keywords | Hilbert space / trace formula / principal function / operator inequality / Shannon inequality / hyponormal operator / Aluthge transform / polar decomposition |
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| Research Abstract |
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.
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