1991 Fiscal Year Final Research Report Summary
Partial *-algebras generated by a family of unbounded operators on Hibert spaces
| Project/Area Number |
02640158
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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 | Fukuoka University |
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Principal Investigator |
INOUE Atsushi Fukuoka University, faculty of Science professor, 理学部, 教授 (50078557)
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| Co-Investigator(Kenkyū-buntansha) |
SENBA Takasi Fukuoka University, faculty of Science Associated professor, 理学部, 講師 (30196985)
KUROSE Hideki Fukuoka University, faculty of Science Associated professor, 理学部, 助教授 (00161795)
AKIYAMA Kenju Fukuoka University, faculty of Science Associated professor, 理学部, 助教授 (70078575)
EBIHARA Yukiyoshi Fukuoka University, faculty of Science professor, 理学部, 教授 (00078601)
TOMITA Minoru Fukuoka University, faculty of Science professor, 理学部, 教授 (10037137)
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| Project Period (FY) |
1990 – 1991
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| Keywords | operator algebra / unbounded operator algebra / partial Op^*-algebra / Tomita-Takesaki theory / cyclic vector / partial *-algebra / non-commutative integration theory / Wightman quantum field theory |
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| Research Abstract |
We have studied a family of unbounded operators equipped with a partial multiplication (partial Op^*-algebra), and obtained the following results :
(1) We studied the structure of partial Op^*-algebras generated by finite commutative symmetric operators.
(2) We studied cyclic vectors for partial Op^*-algebras.
(3) We investigated the self-adjointness and the standardness of (paxtial) Op^*-algebras and unbounded *-representations of *-algebras.
(4) We investigated the self-adjoint extension and standard extension of unbounded *-representations of *-algebras.
(5) We studied invariant positive sesquilinear forms on partial *-algebras and considered the non-commutative integration theory for partial Op^*-algebras.
(6) We extended the Tomita-Takesaki theory for von Neumann algebras to partial Op^*-algebras, and applied it to the Wightman quantum field theory.
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