Classifications of commutative Banach algebras and Banach modules

交换 Banach 代数和 Banach 模的分类

• 批准号: 08640160
• 负责人: TAKAHASI Sin-Ei
• 金额: $ 1.28万
• 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: 1996
• 资助国家: 日本
• 起止时间: 1996 至 1997
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08640160/
• 关键词: commutative Banach algebra; BSE-algbera; Segal algebra; Apostol algbera; Douglas algebra; Gelfand transform; Fourier transform; bounded approximate identity; commutative Banach algebra; Douglas algebra; Fourier transtorm; commutafivc Banach alg

Classifications are based on setting several conditions and considering the classes to satisfy the conditions. This research has been focusing on clarifying the essence of commutative Banach algebras and Banach modules by the following idea : First, they would be classified according to the natural conditions settled, and then whether concrete algebras and modules belong to the classified groups or not, and what invariant properties the specific classified algebra and module have, might be investigated. Before this investigation, based on the above idea we have introduced and investigated the groups respective to BSE-algebras and BSE-Banach modules. In this investigation, we have introduced the new group of commutative Banach algebras named Doss-algebras and developed the general classification theory of the commutative Banach algebras. This general classification theory was based on newly introduced concept referred to quasi-topology. Then, whether the concrete commutative Banach algebras belong to the above two groups respective to the BSE-algebras and the Doss-algebras has been investigated. Furthermore, we have studied on the group of commutative Banach algebras such that the original norm coincides with the BSE-norm and on a certain group of BSE-Banach modules.We have also studied on the group of the commutative Banach algebras of which the greatest regular subalgebra coincides with the Apostol algebras and particularly it is found that the Douglas algebra belongs to such a group and has a certain decomposition based on the natural spectra. In the study of the function which operates on the function space related to the commutative Banach algebra, non-Lipschitz functions which operate or do not operate on non-trivial function space can be characterized successfully. Finally, we have investigated a structure of ring-homomorphism on the commutative Banach algebras, inequality and equality with respect to the Banach norm, and a BKW-operator.

分类基于设定多个条件并考虑满足条件的类别。这项研究一直致力于通过以下想法来阐明交换性Banach代数和Banach模块的本质：首先，它们将根据解决的自然条件进行分类，然后将它们是否属于分类组的组成组和模块是否属于分类组，以及是否不变的属性，以及鉴于特定的分类代数和模块。在研究之前，基于上述思想，我们已经介绍并研究了针对BSE-Elgebras和BSE-Banach模块的组。在这项调查中，我们介绍了名为Doss-Elgebras的新的交换Banach代数，并开发了交换性Banach代数的一般分类理论。该通用分类理论是基于新介绍的概念，称为准故事。然后，研究了混凝土交换的Banach代数属于上述两组，分别属于BSE-Elgebras和Doss-elgebras。此外，我们已经研究了一组可交换的Banach代数，使得原始规范与BSE-NORM和某些BSE-Banach模块相吻合。我们还研究了交换性Banach代数的研究，其中最大的属于Apostol anggerbras的banach代数与Apostol Algebras and and and and and and and and and and and and and and and and and dougn是dough的同时，它是Dough的一小组。基于自然光谱的分解。在对与交换性BANACH代数相关的功能空间运行的功能的研究中，可以成功地表征在非平凡功能空间上运行或不操作的非lipschitz函数。最后，我们研究了对班克代数，关于Banach Norm的不平等和平等的环形摩托形态结构，以及BKW操作员。

项目成果

Osamu Hatori: "Shapiro-Shields type theorem on finitedomain" RIMS Kokyuroku.(to appear).

Osamu Hatori：“有限域上的 Shapiro-Shields 型定理”RIMS Kokyuroku。（即将出现）。

Sin-Ei-Takahasi: "Some convexity constants related to Hlawka inequalities in Banach spaces" RIMS Kokyuroku. (近刊).

Sin-Ei-Takahasi：“与 Banach 空间中的 Hlawka 不等式相关的一些凸性常数”RIMS Kokyuroku（即将出版）。

Sin-Ei-Takahasi: "The proximinality of the center of a quasicentral C^*-algebra" RIMS Kokyuroku. (近刊).

Sin-Ei-Takahasi：“准中心 C^* 代数中心的邻近性”RIMS Kokyuroku（即将出版）。

Sin-Ei Takahasi: "Jensen's inequality and its applications" Hokkaido Univ.Technical Report Series in Mathematics. 48. 66-68 (1997)

Sin-Ei Takahasi：“Jensen 不等式及其应用”北海道大学数学技术报告系列。

Osamu Hatori: "Measures with natural spectra on locally compact abelian groups" Proceeding of the Americal Mathematical Society.(to appear).

Osamu Hatori：“用自然谱对局部紧致阿贝尔群进行测量”美国数学会学报。（待发表）。