Mathematical Sciences: Module Derivations of Banach Algebras

这个数学研究项目的主题是 Banach代数的理论，这可能被认为是 线性代数在无穷多个维度上的应用一 可以在这种设置下进行算术（加法和乘法）， 人们也可以采取限制。一个基本的主题， 这方面的研究是为了了解 和极限行为之间相互影响。比如说， Banach代数之间的映射是否满足 算术恒等式会自动保持极限吗 主要研究人员将研究以下问题： 这种性质。 更具体地说，他们将继续投资- 的连续性和代数结构 从Banach代数到模的导子必要 代数和/或 模块将寻求这将确保每个衍生 是连续的，每一个连续的导子变成一个对偶 双模是内部的，每个连续导子都是 代数的对偶空间是内空间。特别 本文主要研究可积Banach代数 函数和其他自然产生的Banach代数 分析和应用。

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.