2014 Fiscal Year Final Research Report
Spectrum preservers on Banach algebras and the stability of their perturbation
Project/Area Number |
23740097
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Basic analysis
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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)
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Project Period (FY) |
2011-04-28 – 2015-03-31
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Keywords | スペクトル保存写像 / 等距離写像 / 関数環 / 可換Banach環 |
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.
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Free Research Field |
関数環論
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