Mathematical Sciences: Module Derivations of Banach Algebras

数学科学：Banach 代数的模导数

• 批准号: 8803089
• 负责人: Philip Curtis
• 金额: $ 10.13万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-15 至 1991-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8803089&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Module; Derivations; Banach

The subject of this mathematical research project is the theory of Banach algebras, which may be thought of as linear algebra in infinitely many dimensions. One can do arithmetic (add and multiply) in this setting, and one can also take limits. A fundamental theme of research in this area is to understand how the arithmetic and the limit-taking influence one another. For instance, does a map between Banach algebras satisfying prescribed arithmetic identities automatically preserve limits? The principal investigators will work on questions of this nature. More specifically, they will continue their investi- gation of the continuity and algebraic structure of derivations from Banach algebras to modules. Necessary and sufficient conditions on the algebra and/or the module will be sought which will insure that each derivation is continuous, each continuous derivation into a dual bimodule is inner and each continuous derivation into the dual space of the algebra is inner. Particular atention will be paid to Banach algebras of integrable functions and other Banach algebras arising naturally in analysis and applications.

这个数学研究项目的主题是巴纳赫代数理论，它可以被认为是无限多维的线性代数。在此设置中可以进行算术（加法和乘法），也可以进行限制。该领域研究的一个基本主题是了解算术和极限取舍如何相互影响。例如，满足规定算术恒等式的巴纳赫代数之间的映射是否会自动保留极限？ 主要研究人员将致力于解决此类性质的问题。 更具体地说，他们将继续研究从巴拿赫代数到模的推导的连续性和代数结构。将寻求代数和/或模上的必要和充分条件，这将确保每个推导是连续的，到对偶双模的每个连续推导是内部的，并且到代数的对偶空间的每个连续推导是内部的。将特别关注可积函数的巴拿赫代数以及在分析和应用中自然产生的其他巴拿赫代数。