2013 Fiscal Year Final Research Report
Operator space and Its application
| Project/Area Number |
22540220
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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 千葉大学, 理学(系)研究科(研究院), 教授 (50189172)
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| Co-Investigator(Renkei-kenkyūsha) |
伊藤 隆 群馬大学, 教育学部, 教授 (40193495)
松井 宏樹 千葉大学, 大学院理学研究科, 教授 (40345012)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 作用素単調関数 / Pick関数 / 作用素空間 / Haagerupテンソル積 / Schur積 / 作用素の正値性 |
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| Research Abstract |
It is well-known that the theory of matrices is a useful tool for the field of Applied Mathematics. We use the terminology "Operators" as Matrices in infinitely dimensional spaces. In the theory of operators, many unexpected phoenomena occur and such phoenomena do not occur in finitedimensional spaces. In the theory of Operator Algebra or Operators, such phoenomena sometimes occur in the argument in the convergence or not with respect to some norms. We study such facts using the notion of positivity. Operator monotone functions means functions which preserve the order of operators under functional cauculus and monotonicity for matrices is equivalent to that for Operators. We can get the characterization of operator monotonicity for many functions. We also get the characterization of extended Haagerup tensor product for Operator spaces. Using the Schur product of operators, we could realize the result for operator spaces.
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