1989 Fiscal Year Final Research Report Summary
ALGEBRAIC SYSTEMS WHICH RELATE TO OPERATOR ALGEBRA AND RELATED TOPICS
| Project/Area Number |
63540092
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
解析学
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| Research Institution | YAMAGATA UNIVERSITY |
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Principal Investigator |
HAKEDA Josuke YAMAGATA UNIVERSITY, DEPARTMENT OF BASIC TECHNOLOGY, ASSOCIATE PROFESSOR, 工学部, 助教授 (70007003)
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| Co-Investigator(Kenkyū-buntansha) |
SATO Kunio YAMAGATA UNIVERSITY, DEPARTMENT OF BASIC TECHNOLOGY, TEACHING ASSISTANT, 工学部, 助手 (70007194)
TAKAHASHI Sin-ei YAMAGATA UNIVERSITY, DEPARTMENT OF BASIC TECHNOLOGY, ASSOCIATE PROFESSOR, 工学部, 助教授 (50007762)
WATARI Chinami MIYAGIGAKUIN UNIVERSITY, DEPARTMENT OF MATHEMATICS, PROFESSOR, 教養学部, 教授 (80004274)
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| Project Period (FY) |
1988 – 1989
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| Keywords | Jordan triple system / JBW* triple system / quadratic map / quadratic product / Banach algebra / BSE type theorem / Korovkin type theorem / Bernstein polynomial |
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| Research Abstract |
Head investigator mainly worked on an ALGEBRAIC system (Jordan triple system) which include Jordan algebra and operator algebra as its special case. Especially, he researched the relationship between a special triple product (quadratic product) in a Jordan triple system and ALGEBRAIC structure of the system and had the fact that they are deeply related. One result is that a quadratic map (preserving quadratic product and not assuming additivity) preserves norm and the whole real linear structure on essentially non-commutative part of JBW*-triple system. Some results were already published and new progression will be expected.
Investigator Takahashi worked on commutative Banach algebras. For instance, he traced on an analogy of BSE-theorem of group algebra and he had its analogue in commutative Banach algebra. Some results of him are already exposed at some conferences. However, almost of them will be published in this year.
Investigator Sato studied Bernstein polynomial and checked the rate of convergence in a few different functional spaces.
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