2004 Fiscal Year Final Research Report Summary
A Class of unbounded ^*-representations constructed from unbounded C^*-seminorms
| Project/Area Number |
15540223
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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) |
KUROSE Hideki Fukuoka Univ., Fac. Sci., Professor, 理学部, 教授 (00161795)
OGI Hidekazu Fukuoka Institute of Technology, Fac. Engine, Associate Professor, 工学部, 助教授 (30248471)
IKEDA Itsuko Fukuoka Univ., Fac. Sci., Assistant, 理学部, 助手 (10268972)
TAKAKURA Mayumi Fukuoka Univ., Fac. Sci, Assistant, 理学部, 助手 (40268975)
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| Project Period (FY) |
2003 – 2004
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| Keywords | O^*-algebras / partial O^*-aleebras / unbounded ^*-representations / unbounded C^*-seminorms / well-behaved ^*-representations / spectral unbounded C^*-seminorms / spectral ^*-representations / conditional expectations of O^*-algebras |
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| Research Abstract |
Unbounded ^*-representations of ^*-algebras constructed from unbounded C^*-seminormLs have been studied. We (Bhatt-Inoue-Ogi) showed that it was possible to construct a class of unbounded ^*-representations from unbounded C^*-seminorms, and defined the notion of well-behaved ^*-representations which is nice in its class. In particular, we have characterized the existence of well-behaved ^*-representations and that of spectral well-behaved ^*-representations. Furthermore, we have proceed studies of general unbounded operator algebras (O^*-algebras and partial O*-algebras). We have investigated the following:
(1) The existence of well-behaved ^*-representations constructed from unbounded C^*-seminorms.
(2) Applications to locally convex ^*-algebras.
(3) The studies of the structure and representation theory of (locally convex) ^*-algebras with spectral unbounded C^*-seminorms.
(4) The existence of spectral well-behaved ^*-representations.
(5) The study of weights on (partial) O^*-algebras.
(6) Derivations of (partial) O^*-algebras.
(7) Conditional expectations of O^*-algebras.
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