1998 Fiscal Year Final Research Report Summary
On the properties of adjacency operators of graphs and the maps between von Neumann algegras
| Project/Area Number |
09640147
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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 |
解析学
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| Research Institution | Miyagi University of Education |
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Principal Investigator |
TAKEMOTO Hideo MIYAGI UNIV.OF EDUCATION,EDUCATION,PROFESSOR, 教育学部, 教授 (00004408)
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| Co-Investigator(Kenkyū-buntansha) |
MORIOKA Masaomi MIYAGI UNIV.OF EDUCATION,EDUCATION,ASSIT.PROFESSOR, 教育学部, 助教授 (10174400)
YAMADA Haruki MIYAGI UNIV.OF EDUCATION,EDUCATION,PROFESSOR, 教育学部, 教授 (00092578)
YOROZU Sinsuke MIYAGI UNIV.OF EDUCATION,EDUCATION,PROFESSOR, 教育学部, 教授 (40019849)
SHIRAI Susumu MIYAGI UNIV.OF EDUCATION,EDUCATION,PROFESSOR, 教育学部, 教授 (30115175)
AZUMA Kazuoki MIYAGI UNIV.OF EDUCATION,EDUCATION,PROFESSOR, 教育学部, 教授 (70005776)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Von Neumann algebra / Generation / Directed graph / Adjacency operator / De Morgan / Spectral radius / Numerical radius / Norm |
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| Research Abstract |
We had some new interesting results in these two years. For the generation of von Neumann algegras which was one of the purposes on the occasion of the application of this research, we had some results. One of these is the following : We could show that the von Neumann algebra generated by the adjacency operator respect to a regular directed graph being an partially isometric operator is always the von Neumann algebra of type I.Second of the results is the following : We solved the conjecture by Saito where can we a power partial isometric operator generated the von Neumann algebra with any given type, For the answer for this Saito's problem. we could show that the von Neumann algebra generated by any power partial isometric operator is a von Neumann algebra of type I.Furthermore, me could give a characterization of the power partial isometric operators which is a different from the characterization given before. And an idea of the proof for this characterization had an important role for the proof of Saito's problem.
We could give a characterization of de Morgan algebras and Kleene algebrlas by introducing a new notation. This new notation was considered when we examine the properties of the mapping between the von Neumann algebras and me expect that this notation will be a useful role for making the research of the property between the von Neumann algebras. Furthermore, we could introduce a new notation-of the isoperimetric number of the directed infinite graphs and we showed the relation of spetral radius, numerical radius and norm of adjacency operator respect to the directed infinite graph. Furthermore, we investigated the property of folliation connected with the research of structure of non-commutative geometry in operator algebras.
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