2010 Fiscal Year Final Research Report
Certain spectra preserving maps on Banach algebras and the stability of their perturbations
| Project/Area Number |
19740063
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Yamagata University |
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Principal Investigator |
MIURA Takeshi 山形大学, 大学院・理工学研究科, 教授 (90333989)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 関数解析学 / Banach環 / スペクトル保存 / 摂動と安定性 |
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| Research Abstract |
Molnar investigated, what is so called "multiplicatively spectra preserving maps" between C^*-algebras, and characterized such maps. We generalized the result by Molnar to such maps between unital, semisimple commutative Banach algebras. In addition, we proved that quite similar results to the above hold for "peripherally multiplicative maps" and "spectra radii preserving maps". We also investigated some differential equations in Banach space-valued function spaces, and gave a sufficient condition in order that Hyers-Ulam or Ger type stability hold.
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