Classifications of commutative Banach algebras and Banach modules and its applications

交换Banach代数和Banach模的分类及其应用

• 批准号: 22540168
• 负责人: TAKAHASI Sin-ei
• 金额: $ 2.5万
• 依托单位: Toho University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540168/
• 关键词: commutative Banach algebra; Segal algebra; convolution measure algebra; quasi-topology; approximate identity; Hyers-Ulam stability; inequality; Banach algebra; BSE and BED; Fourier algebra; fixed point theorem; Ulam type stability; additive ma

I n 1990, the author and the cooperation researchers, Prof. O. Hatori, introduced the class called BSE-algebras. In the present study, the author has successfully classified commutative Banach algebras by using the new concept that is called quasi-topology originating from BSE-algebras. Especially, with this classification, the author made clear the position of important commutative Banach algebras called Segal algebras. In addition, as applications of this classification, certain Ulam type stability problems are solved and several inequalities are derived for convex functions.

1990年，作者和合作研究人员O.Hatori教授引入了BSE-代数类。在本研究中，作者利用源于BSE-代数的拟拓扑的新概念，成功地对交换Banach代数进行了分类。特别地，通过这种分类，作者明确了重要的交换Banach代数--西格尔代数的地位。此外，作为这种分类的应用，我们还解决了一些Ulam型稳定性问题，并得到了凸函数的几个不等式。

项目成果

An equality condition of Arhippainen-Muller's estimate and its related problem

Arhippainen-Muller估计的等式条件及其相关问题

• 期刊: Taiwanese J.Math. (近刊(印刷中))
• 作者: Sin-Ei Takahasi;Takeshi Miura;Takahiro Hayata
• 通讯作者: Takahiro Hayata

Characterization of a generalized triangle inequalities in normed spaces

赋范空间中广义三角不等式的表征

• 发表时间: 2012
• 期刊: Nonlinear Analysis: Theory, Methods and Applications
• 作者: Farzad Dadipour;Mohammad Sal Moslehian;John M.Rassias and Sin-Ei Takahasi
• 通讯作者: John M.Rassias and Sin-Ei Takahasi

A new interpretation of Chebyshev's inequalities for sequences of real numbers and quasi-arithmetic means

实数序列切比雪夫不等式的新解释和准算术方法

• 发表时间: 2012
• 期刊: Journal of Mathematical Inequalities
• 影响因子: 2.9
• 作者: Yasuo Nakasuji;Keisaku Kumahara and Sin-Ei Takahasi
• 通讯作者: Keisaku Kumahara and Sin-Ei Takahasi

A new interpretation of Jensen's inequality and geometric properties of ψ-means

Jensen 不等式和 ψ 均值几何性质的新解释

• 发表时间: 2011
• 期刊: Journal of Inequalities of Applications
• 作者: Yasuo Nakasuji;Keisaku Kumahara;Sin-Ei Takahasi
• 通讯作者: Sin-Ei Takahasi

難しい事を簡単に言ってみたいが-Aτ環を例にとって-

我想用简单的语言解释一些困难的事情——以 Aτ 环为例——

• 发表时间: 2010
• 作者: 井上潔司;安芸重雄;平野勝臣;下村勝孝;安芸重雄;高橋眞映;Katsunori Shimomura;安芸重雄;高橋眞映
• 通讯作者: 高橋眞映