2010 Fiscal Year Final Research Report
A study on trace-rank inequality concerned with module structure of complex Hardy spaces
| Project/Area Number |
21740099
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Shimane University |
|---|
Principal Investigator |
SETO Michio Shimane University, 総合理工学部, 講師 (30398953)
|
|---|
| Project Period (FY) |
2009 – 2010
|
| Keywords | 関数解析 / ハーディ空間論 / 作用素論 / 多変数作用素論 |
|---|
| Research Abstract |
(1) Since Hardy spaces can be seen as Hilbert modules over the polynomial ring, a Hilbert function can be defined for every submodule. We succeeded in giving an explicit formula for Hilbert functions of submodules in a certain class.
(2) As a sequel of (1), we introduced perturbation theory for linear operators to our research field. As a result, we have obtained a new viewpoint, which can be applied to other Hilbert function spaces.
|
