Spectrum preservers on Banach algebras and the stability of their perturbation

2014 Fiscal Year Final Research Report

• 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
• 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.

Free Research Field

関数環論