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2018 Fiscal Year Final Research Report

A study of geometric structure of Banach spaces and its applications

Research Project

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Project/Area Number 15K04920
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionNiigata University

Principal Investigator

SAITO KICHI-SUKE  新潟大学, 自然科学系, フェロー (30018949)

Co-Investigator(Kenkyū-buntansha) 加藤 幹雄  信州大学, 工学部, 非常勤講師 (50090551)
三谷 健一  岡山県立大学, 情報工学部, 准教授 (00468969)
渡邉 恵一  新潟大学, 自然科学系, 教授 (50210894)
Project Period (FY) 2015-04-01 – 2019-03-31
Keywordsバナッハ空間 / James定数 / Birkhoff直交 / Radon空間
Outline of Final Research Achievements

In the study of geometry of Banach spaces, two notions of orthogonality and geometric constant are important. First, we sucessed to characterize 2 dimensional Banach spaces with James constant √2. We published three papers (Math Nach, Mediter J Math, Math Inequal Appl) about this results. In the study of symmetry of Banach spaces, we studied the symmetric points of von Neumann algebras and so on. In particular, we characterized symmetric 2-dimmensional Banach spaces using generalized Day-James spaces.

Free Research Field

バナッハ空間論

Academic Significance and Societal Importance of the Research Achievements

バナッハ空間における幾何学構造について、特に、2次元空間の構造がまだ解明されていなかったが、absoluteノルム空間の概念を用いて、その解明に成功した。それにより、抽象的だった、Radon空間がDay-James 空間を用いて、特徴付けしたことには、大きな意義がある。

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Published: 2020-03-30  

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