2002 Fiscal Year Final Research Report Summary
Unbounded *-representations of partial *-algebras
| Project/Area Number |
13640228
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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 |
Global analysis
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| Research Institution | Fukuoka University |
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Principal Investigator |
INOUE Atsushi Fukuoka Univ., Fac. Sci., Professor, 理学部, 教授 (50078557)
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| Co-Investigator(Kenkyū-buntansha) |
OGI Hidekazu Fukuoka Institute of Tech Univ., Fac. Engin., Associate Professor, 工学部, 助教授 (30248471)
NAGAMACHI Shigeaki Tokushima Univ., Fac. Engin., Professor, 工学部, 教授 (00030784)
KUROSE Hideki Fukuoka Univ., Fac. Sci., Professor, 理学部, 教授 (00161795)
TAKAKURA Mayumi Fukuoka Univ., Fac. Sci., Research Assistant, 理学部, 助手 (40268975)
IKEDA Itsuko Fukuoka Univ., Fac. Sci., Research Assistant, 理学部, 助手 (10268972)
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| Project Period (FY) |
2001 – 2002
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| Keywords | O^*-algebras / partial O^*-algebras / unbounded *-representations / unbounded D^*seminorms / weights / well-behaved *-representations |
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| Research Abstract |
*-algebras (O^*-algebras) of closable operators in Hilbert space have been studied from the pure mathematical situation and the physical applications. A survey of the theory of O^*-algebras may be found in the monograph of K. Schmudgen "Unbounded Operator Algebras and Representation Theory, Operator Theory: Advances and Applications vol. 37, Birkhauser(1990)" and the lecture note of A. Inoue "Tomita-Takasaki Theory in Algebras of Unbounded Operator Algebras, Lecture Notes in Mathematics, 1699, Springer(1995)".
Furthermore, partial *-algebras (partial O^*-algebras) of closable operators have been studied from the mathematical situations and the physical applications, but it seems that the systematic studies are insufficient. In order to proceed the studies of *-representations of partial *-algebras, we have investigated the following.
(1) What is a well-behaved *-representation in unbounded *-representations of (partial) *-algebras?
(2) Systemic studies of weights of partial O^*-algebras.
(3) Applications of (1) and (2) to quantum physics.
Thus we (A. Inoue, J. P. Antoine and C. Trapani) have published a book "Partial *-algebras and Their Operator Realizations, Mathematics and Its Applications vol. 553" from Kluwer Academic Publishers.
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Research Products
(14 results)
