Classifications of commutative Banach algebras and Banach modules

交换 Banach 代数和 Banach 模的分类

• 批准号: 10640150
• 负责人: TAKAHASI Sin-ei
• 金额: $ 1.54万
• 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: 1998
• 资助国家: 日本
• 起止时间: 1998 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640150/
• 关键词: commutative Banach algebra; BSE-algbera; Segal algebra; Apostol algebra; Fourier multiplier algebra; Gelfand transform; bounded weaka approximate identity; Hlawka type inequalities; ring homomorphism; Hadamard product; Hlawka inequality; Djokov

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 research, a necessary and sufficient condition for a concrete Segal algebra on a locally compact abelian group to be BSE has been given. We further give a constraction of a minimal bounded weak approximate identities for these algebra. We also show that the greatest regular closed subalgebra and Apostol algebras of semisimple commutative Banach algebras are charaterized in terms of level sets of the maximal ideal spaces. Also the commutative Banach algebra of all Fourier multipliers on the Euclidian space which have have natural spectra has been investigated. Furthermore the relations between all measures with natural spectra on a compact abelian group and Apostol algebra has been considered and it is shown that both do not coincide with each other in the discrete case.Finally, we have investigated a structure of ring-homomorphism on the unital semisimple commutative Banach algebras, a generalization of Mond-Pecauic's theorem on the converse of Jensen's inequality, Hadamard product versions of operator inequalities associated with extensions of Holder- McCarthy-Kantorovich inequality and Hlawka type inequalities on Banach spaces.

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。在这项研究中，已经给出了在本地紧凑的阿贝尔群体上的混凝土塞加尔代数为BSE的必要条件。我们进一步给出了这些代数的最低限制的弱近似身份的收缩。我们还表明，半常规的封闭亚位bra和Apostol代数的半粘合性Banach代数以最大理想空间的水平集为特征。还研究了具有天然光谱的欧几里得空间上所有傅立叶乘数的交换性Banach代数。 Furthermore the relations between all measures with natural spectra on a compact abelian group and Apostol algebra has been considered and it is shown that both do not coincide with each other in the discrete case.Finally, we have investigated a structure of ring-homomorphism on the unital semisimple commutative Banach algebras, a generalization of Mond-Pecauic's theorem on the converse of Jensen's inequality, HADAMARD产品版本的运营商不平等现象与Holder-McCarthy-Kantorovich不平等和Hlawka型不平等相关的扩展相关。

项目成果

J.Micic: "Inequalities of Furuta and Mond-Pecaric" Mathematical Inequalities & Applications. 2-1. 83-111 (1999)

J.Micic：“Furuta 和 Mond-Pecaric 的不等式” 数学不等式

原卓哉: "A weighted extension of Carleman's ineqaulity"京都大学数理解析研究所講究録. 1136. 37-44 (2000)

Takuy​​a Hara：“卡尔曼不等式的加权扩展”京都大学数学科学研究所 Kokyuroku。1136. 37-44 (2000)。

Yuki Seo: "Inequalities of Furuta and Mond-Pecaric on the Hadamard product"Journal of Inequalities and Applications. 5-3. 263-285 (2000)

Yuki Seo：“Furuta 和 Mond-Pecaric 关于 Hadamard 产品的不等式”不等式与应用杂志。

高橋泰嗣: "Hlawka type inequalities in Banach spaces"京都大学数理解析研究所講究録. 1136. 90-95 (2000)

Yasushi Takahashi：“Banach 空间中的 Hlawka 型不等式”京都大学数学科学研究所 Kokyuroku。1136. 90-95 (2000)。

Sin-Ei Takahasi: "A structure of ring homomorphisms on commutative Banach algebras"Proceedings of the American Mathematical Society. 127-8. 2283-2288 (1999)

Sin-Ei Takahasi：“交换巴纳赫代数上的环同态结构”美国数学会论文集。