2007 Fiscal Year Final Research Report Summary
Unbounded^*-representations and their applications of quantum physics
| Project/Area Number |
18540225
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Global analysis
|
|---|
| Research Institution | Fukuoka University |
|---|
Principal Investigator |
INOUE Atsushi Fukuoka University, Fac. Sci., Professor (50078557)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
KUROSE Hideki Fukuoka University, Fac. Sci., Professor (00161795)
OTA Shoichi Kyushu Univ., Graduate School of Design, Professor (70107176)
OGI Hidekazu Fukuoka Institute of Tech. Univ., Fac. Engine, Associate Professor (30248471)
|
|---|
| Project Period (FY) |
2006 – 2007
|
| Keywords | unbounded *-representations / C*-algebras / non-commutative geometry / O*-algebras / partial O*-algebras |
|---|
| Research Abstract |
81. A. Inoue, S.J. Bhatt and M Fragoulopoulou studied well-behaved representations of (locally convex) *-algebras. In particular, Inoue and Fragoulopoulou studied well-behaved *representations of (locally convex) *-algebras. Inoue, S. Ota and H.Kurose applied them to quantum groups.
2. Inoue, F.Bagarello, Fragoulopoulou, K.D. Kursten and C. Trapani studied the algebraic structure and representation of locally convex *-algebra A[τ] containing C*-algebra A. In particular, we defined locally convex quasi C*-algebras which are a generalization of C*-algebras to locally convex quasi *-algebras, and proceeded the studies of their structures and representations.
3. Inoue and Bhatt studied noncommutative differential structure in C*-algebras. We investigated the spectral invariance, the C^∞-functional calculus of differential algebras introduced by Blackadar and Cuntz. Furthermore, we studied smooth subalgebras in C*-algebras and C*-structure.
4. Inoue, H.Ogi and M. Takakura considered a generalization of conditional expectations for von Neumann algebras to those for O*-algebras. We defined and investigated the notions of weak conditional expectations and unbounded conditional expectations of O*-algebras. In particular, we investigated under which conditions an unbounded conditional expectation is a conditional expectation.
5. Inoue, Bagarello, Trapani studied completely positive maps of O*-algebras and derivations of O*-algebras.
|
