Study on von Neumann algebras, free probability and non-commutative function spaces
| Project/Area Number |
24540214
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Global analysis
|
|---|
| Research Institution | Kyushu University |
|---|
Principal Investigator |
UEDA Yoshimichi 九州大学, 数理(科)学研究科(研究院), 准教授 (00314724)
|
|---|
| Project Period (FY) |
2012-04-01 – 2016-03-31
|
| Project Status |
Completed (Fiscal Year 2015)
|
| Budget Amount *help |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
|---|
| Keywords | フォンノイマン環 / 自由積 / 軌道自由エントロピー / 前共役 / 自由確率論 / 情報量 / III型 / 非可換ハーディー空間 / 自由エントロピー / 非可換 L1-空間 |
|---|
| Outline of Final Research Achievements |
I clarified the structure of free product von Neumann algebras from various viewpoints. Especially, I identified the resulting free product von Neumann algebras with a certain explicit one under some conditions. Also, we computed several invariants for free product von Neumann algebras in the general setup, and obtained a result on the positional rigidity for subalgebras as well as a uniqueness result for the free product decomposition. I studied the orbital free entropy. In particular, we made some nontrivial computation of it. We also introduced the concept of pressure related to the orbital free entropy motivated by statistical physics and investigated its relation to random matrices. Moreover, I generalized the previous definition of orbital free entropy and discussed its general properties. Finally, we studied von Neumann algebra preduals and investigated a strong property, which is rather opposite to uniform convexity, for them.
|
Report
(5 results)
Research Products
(19 results)
-
-
-
-
-
-
-
-
-
-
-
-
[Presentation] Orbital free entropy2013
Author(s)
Yoshimichi Ueda
Organizer
AMS-RMS joint meeting, Special session: Random matrices and free probability
Place of Presentation
"1 Decembrie 1918" University of Alba Iulia, Romania
Related Report
Invited
-
-
-
-
-
-
-
