Classifications of commutative Banach algebras and Banach modules and its applications

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400120
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Toho University
• Principal Investigator: TAKAHASI Sin-ei 東邦大学, 理学部, 訪問教授 (50007762)
• Co-Investigator(Kenkyū-buntansha): TSUKADA Makoto 東邦大学, 理学部, 教授 (10120198) ; KOBAYASHI Yuji 東邦大学, 理学部, 訪問教授 (70035343)
• Co-Investigator(Renkei-kenkyūsha): HATORI Osamu 新潟大学, 自然科学系, 教授 (70156363)
• Research Collaborator: MIURA Takeshi 新潟大学, 自然科学系, 教授 (90333989) ; TAKAGI Hiroyuki 信州大学, 理学部, 教授 (20206725)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: Banach algebra / Segal algebra / Fourier algebra / Lau algebra / quasi-topology / Hyers-Ulam stability / inequality / topological semigroup

Outline of Final Research Achievements

We have studied commutative Banach algebras successfully by introducing a
new notion of quasi-topology. It was started by the introduction of the class BSE by Takahasi and Hatori, and it guided us to dividing commutative Banach algebras into 4 classes. In cooperation with J. Inoue, we further have claried BSE and BED properties of abstract Segel algebras which extend the Segal algebras on locally compact abelian groups by Reiter to commutative Banach algebras and of new Segel algebras induced by local A-functions.
We applied these results to solutions of a decision problem related to multipliers of Lau algebras constructed by semisimple commutartive Banach algebras, of stability problems related to the Ulam-type stability, of certain inequalities on convex functions and of the structure of topological semigroups on the real numbers.

Free Research Field

数物系科学