Research on topological and geometrical structure of invariant subspace problem based on a choice function
| Project/Area Number |
16K13760
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Ibaraki University |
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Principal Investigator |
hirasawa go 茨城大学, 理工学研究科(工学野), 教授 (10434002)
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 不変部分空間 / 半閉部分空間 / 区間縮小法 / 線形次元 / path / 作用素幾何平均 |
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| Outline of Final Research Achievements |
Although the goal of creating a roadmap to solve the invariant subspace problem on a separable Hilbert space, or finding a clue to a solution could not be achieved, I obtained some results which couled be linked to the future. Results we obtained are on the choice function that appears in the our method of this research and on semi-closed subspaces. As a main result, we introduced a path connecting two semi-closed subspaces using Uhlmann's interpolation operator means, and obtained results on a invariant property of a path. By considering the p-geometric operator mean as an interpolation operator mean, new findings could be obtained.
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| Academic Significance and Societal Importance of the Research Achievements |
不変部分空間問題（ISPと略記）は、J.von Neumann の時代から世界の多くの数学者によって長い間研究されてきており、様々な研究成果があるが、未だに完全には解決されていない。線形代数の延長上に位置するISPは、数学の基盤問題として学術的に意義があり、この問題を解決することは多くの数学者に注視されることでもあるため、社会的意義も大きいと考えられる。本研究成果は、新しい視点からアプローチを行うための途中経過の位置付けである。
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Report
(4 results)
Research Products
(4 results)
