| Project/Area Number |
15540198
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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 |
Global analysis
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| Research Institution | Chiba University |
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Principal Investigator |
NAGISA Masaru Chiba University, Faculty of Science, Professor, 理学部, 教授 (50189172)
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| Co-Investigator(Kenkyū-buntansha) |
ISHIMURA Ryuichi Chiba University, Faculty of Science, Professor, 理学部, 教授 (10127970)
MATUI Hiroki Chiba University, Graduate School of Science and Technology, Assistant, 大学院・自然科学研究科, 助手 (40345012)
ITOH Takashi Gunma Univ., Faculty of Education, Professor, 教育学部, 教授 (40193495)
WADA Shuhei Kisarazu National College of Tech, Associate Professor, 助教授 (00249757)
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| Project Period (FY) |
2003 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥3,100,000 (Direct Cost: ¥3,100,000)
Fiscal Year 2005: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2004: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2003: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | completely positive map / completely bounded map / operator space / numerical radius / Schur multiplier / Haagerup tensor product / numerical radius operator space / operator algebra / シュア-積 / モジュール写像 / 可換子表現 / 写像の分解 |
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| Research Abstract |
Our interest of this research is in the intersection area of Operator Theory and Operator Algebra.
One of main results is to characterize the numerical radius norm of Schur multipiers. U.Haagerup refound the characterization of the norm of Schur multiplier and he constructed the theory of Haagerup tensor product of operator spaces. T.Ando proved the similar characterization of the numerical radius norm of Schur multipliers for matrices. Our result is extended vesion of Ando's result.
Next result is concerned with operator spaces. As an application of abobe result, we consider linear spaces with matrix norms. Usual norms implies the structure of operator spaces. We consider numerical radius norms instead of usual norms. We call it numerical radius operator space. Z.-J.Ruan proved that every operator spaces can be realized as a subspace of B(H) with usual norms, where B(H) is the set of all bounded linear operators on a Hilbert space H. We can show the similar result for numerical radius operator spaces, that is, every numerical radius operator spaces can be realized as a subspace of B(H) with numerical radius norms. This result contains Ruans' result as a special case.
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