Spectrum preservers on Banach algebras and the stability of their perturbation
Project/Area Number |
23740097
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
Basic analysis
|
Research Institution | Niigata University (2013-2014) Yamagata University (2011-2012) |
Principal Investigator |
MIURA TAKESHI 新潟大学, 自然科学系, 教授 (90333989)
|
Project Period (FY) |
2011-04-28 – 2015-03-31
|
Project Status |
Completed (Fiscal Year 2014)
|
Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
Keywords | スペクトル保存写像 / 等距離写像 / 関数環 / 可換Banach環 / 摂動の安定性 / スペクトル保存 |
Outline of Final Research Achievements |
I investigated the structure of mappings which preserve spectra or related information between Banach algebras in detail. I gave a characterization of surjective isometries without assuming linearity between function algebras, which need not be unital. Many results on multiplicatively peripheral spectrum preserving surjections are well known. I generalized some of them and proved the structure theorem on spectra radii preserving mappings between unital semi-simple commutative Banach algebras. I gave a necessary and sufficient condition for a system of Banach space valued differential equations to be stable in the sense of Hyers and Ulam. I also gave a sufficient condition for an integral equation to have the Hyers-Ulam stability.
|
Report
(5 results)
Research Products
(31 results)
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
[Presentation] 関数空間上の全射等距離写像2014
Author(s)
三浦 毅
Organizer
集合論的・幾何学的トポロジーと種々の分野の交流
Place of Presentation
京都大学数理解析研究所(京都府・京都市)
Year and Date
2014-10-23
Related Report
Invited
-
-
-
-
-
[Presentation] Isometries between function spaces
Author(s)
H. Koshimizu, T. Miura, H. Takagi and S.-E. Takahasi
Organizer
Complex Analysis and Applications '13
Place of Presentation
The Institute of Mathematics and Informatics, Bulgaria
Related Report
Invited
-
-
-
-
-