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: 19540159
• 负责人: TAKAHASI Sin-Ei
• 金额: $ 2.5万
• 依托单位: Yamagata University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19540159/
• 关键词: commutative Banach algbera; Segal algbera; convolution measure algbera; quasi-topology; approximate identity; Hyers-Ulam stability; inequality; commutative Banach algebra; Gelfand transform; uniform algebra; Peripheral spectrum; convolution mea

The author and coauthor succeeded in classifying commutative Banach algebras more closely by using the notion of quasi topology, which is originated from certain classes of Banach algebras introduced by the authors in 1990. In addition, the authors investigated classes for some concrete commutative Banach algebras. As applications, the authors solved certain stability problems and obtained several inequalities.

作者和合作者利用准拓扑的概念成功地对可交换的Banach代数进行了更紧密的分类，该概念来源于作者在1990年引入的Banach代数的某些类别。此外，作者还研究了一些具体可交换巴拿赫代数的类。作为应用，求解了若干稳定性问题，得到了若干不等式。

项目成果

Peripherally monomial-preserving maps between uniform algebras

均匀代数之间的外围单项式保留映射

• 发表时间: 2009
• 期刊: Mediterr.J.Math. 6-1
• 作者: Osamu Hatori;Kazumi Hino;Takeshi Miura;Hirokazu Oka
• 通讯作者: Hirokazu Oka

Stability of almost multiplicative functionals

几乎乘法函数的稳定性

• 期刊: Aust.J.Math.Anal.Appl. (近刊(印刷中))
• 作者: Norio Niwa;Hirokazu Oka;Takeshi Miura;Sin-Ei Takahasi
• 通讯作者: Sin-Ei Takahasi

関数環上のある種の値域保存写像

函数环上的某些范围保留映射

• 发表时间: 2007
• 作者: 高橋眞映;三浦 毅;高橋眞映;羽鳥理
• 通讯作者: 羽鳥理

An estimate of the commutativity of C^2-functions and probability measures

C^2 函数的交换性估计和概率测度

• 发表时间: 2009
• 期刊: Math.Inequal.Appl. 3-2
• 作者: Takeshi Miura;Takahiro Hayata;Sin-Ei Takahasi
• 通讯作者: Sin-Ei Takahasi

Peripheral multiplicativity of maps on uniformly closed algebras of continuous functions which vanish at infinity

无穷远消失的连续函数的一致闭代数映射的外围乘性

• 发表时间: 2009
• 期刊: Tokyo J.Math. 32-1
• 作者: Osamu Hatori;Takeshi Miura;Hirokazu Oka;Hiroyuki Takagi
• 通讯作者: Hiroyuki Takagi