| Project/Area Number |
16K05168
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Gunma University |
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Principal Investigator |
ITOH TAKASHI 群馬大学, 教育学部, 教授 (40193495)
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| Research Collaborator |
Nagisa Masaru
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| Project Period (FY) |
2016-10-21 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2018: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
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| Keywords | 数域半径 / 完全有界写像 / 作用素環 / ヒルベルト空間 / 作用素空間 / 関数解析 / 作用素論 |
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| Outline of Final Research Achievements |
Inspired the equivalence between the factoring problem of operators using the extended numerical radius and the embedding problem of finite factors posed by Connes, we have reached to the key if the factored operator can be replaced by the
operator inside the given operator algebra.
We approached the goal as the factoring problem of the completely bounded map from a C*-algebra generated by the free group to its dual space. It was possible to factor the map. If the map shown up can be factored, the longstanding above problem will be settled down. However we can show that the operator is in a von- Neuman algebra at present.
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| Academic Significance and Societal Importance of the Research Achievements |
バナッハ空間論において古典的な問題であるヒルベルト空間を経由する分解問題が、２つのヒルベルト空間を経由する分解問題として作用素環論の研究の中に現われ、数域半径が、新たな視点を与えることが、明確になってきた。この問題を作用素環論の研究に端を発した作用素空間の視点から捉え直すことを目的とした新しい方向性をもつ研究である。Connesのopen problem に対するアプローチは多様であるが、数域半径と分解問題としてとらえたことに斬新さを有する。
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