Studies on structures and isometries of commutative Banach algebras

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540193
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Shinshu University
• Principal Investigator: TAKAGI Hiroyuki 信州大学, 学術研究院理学系, 教授 (20206725)
• Co-Investigator(Kenkyū-buntansha): HATORI Osamu 新潟大学, 自然科学系, 教授 (70156363)
• Co-Investigator(Renkei-kenkyūsha): MIURA Takeshi 新潟大学, 自然科学系, 教授 (90333989) ; UEKI Sei-Ichiro 茨城大学, 工学部, 准教授 (70512408)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 関数解析学 / バナッハ環 / 保存問題 / 合成作用素

Outline of Final Research Achievements

Inspired by the preserver problem of Banach algebras, we consider the characterization of (not necessarily linear) isometries between continuous function spaces. Here a continuous function space means a linear space consisting of (not necessarily all) continuous functions with the supremum norm. We prove that if continuous function spaces A and B satisfy a certain separation property, then every isometry from A onto B is represented by using a weighted composition operator and its complex conjugate on the Choquet boundary of B.

Free Research Field

数学（基礎解析学）