| Project/Area Number |
07454020
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
解析学
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| Research Institution | HOKKAIDO UNIVERSITY |
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Principal Investigator |
KISHIMOTO Akitaka Hokkaido Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (00128597)
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| Co-Investigator(Kenkyū-buntansha) |
YOSHINO Takashi Tohoku Unvi.Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (50005774)
YAMANOUCHI Takehiko Hokkaido Univ., Grad.School of Sci., Associate Prof., 大学院・理学研究科, 助教授 (30241293)
ARAI Asao Hokkaido Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (80134807)
HAYASHI Mikihiro Hokkaido Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (40007828)
NAKAZI Takahiko Hokkaido Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (30002174)
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| Project Period (FY) |
1995 – 1996
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| Project Status |
Completed (Fiscal Year 1996)
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| Budget Amount *help |
¥7,000,000 (Direct Cost: ¥7,000,000)
Fiscal Year 1996: ¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 1995: ¥3,600,000 (Direct Cost: ¥3,600,000)
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| Keywords | Hardy spaces / Bergman spaces / Toeplitz operators / Dirac operators / C^<**>-algebras / von Neumann algebras / automorphisms / bounded analytic functions / Beraman空間 / 作用素環 / 自己同型写像 / ローリンの性質 / 共役類 / ホモトピー類 / KK理論 / 量子系 / 古典系 |
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| Research Abstract |
Ever since the advent of quantum mechanics we have treated non-commutative objects more and more often but their contents range wildly. We investigate various function spaces, some operators on these spaces, Hamiltonians and Dirac operators, relations and inequalities among operators, algebras of operators, automorphisms of these algebras, groups of automorphisms, actions and coactions of groups, representations of quantum groups etc. The head investigator considered the problem of quantizing the so-called Rohlin property in ergodic theory in the contents of C^<**>-algebras and their automorphisms. Since we must use norm topology, the present definition of the Rohlin property imposes strong restrictions on the algebras and automorphisms (compared with the von Neumann algebra case), which may suggest a further generalization is desirable. But as far as we stick to the present definition, we seem to have reached general results.
Further results are as follows : A generalization is attempted for a result of abundance of pure in-variant states which makes a sharp contrast between classical and quantum mechanics (Kishimoto). Various function spaces such as Hardy and Bergman spaces, such operators as Toeplitz operators and the problem of invariant subspaces are investigated (Nakazi). The problem of separation of points are studied for bounded analytic functions (Hayashi). Hamiltonians of various models, repre-sentations of canonical commutation relations, and representations of quantum groups are analized (Arai). Classification of coactions of finite groups on von Neumann algebras are attempted (Yamanouchi).
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