Properties of Banach algebras and their extensions

Banach代数的性质及其推广

• 批准号: 2438047
• 金额: --
• 依托单位: University of Nottingham
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2438047
• 关键词: Properties; Banach; algebras; their; extensions

Banach algebras can have many different properties. Two contrasting examples are the algebra of all continuous complex-valued functions on the closed unit disc, and the subalgebra of this algebra consisting of those functions which are continuous on the closed disc and analytic on the interior of the disc. In the second of these algebras, any function which is zero throughout some non-empty open set must be constantly zero. This is very much not the case in the bigger algebra: indeed Urysohn's lemma shows that for any two disjoint closed subsets of the closed disc, there is a continuous, complex-valued function defined on the disc which is constantly 0 on one closed set and constantly 1 on the other (algebras of this type are called regular algebras).Most commutative Banach algebras have some features in common with one or the other of these two algebras. The aim of this project is to investigate a variety of conditions (including regularity conditions) for Banach algebras, especially Banach function algebras, to relate these conditions to each other, and to other important conditions that Banach algebras may satisfy, and to investigate the preservation or introduction of these conditions when you form various types of extension of the algebras (especially 'algebraic' extensions such as Arens-Hoffman or Cole extensions).

Banach代数可以具有许多不同的特性。两个对比的例子是封闭的单位盘上所有连续复合物值函数的代数，以及该代数的子代数由这些函数组成，这些功能是在封闭盘上连续的，在盘内部的封闭盘和分析。在这些代数的第二个中，任何一个非空的开放式设置中的任何函数都必须持续为零。在较大的代数中，情况并非如此：确实，乌里索恩的引理表明，对于任何两个隔离光盘的隔离式闭合子集，在碟片上定义了一个连续的，复杂的值定义的功能，在一个封闭式上不断地定义为0，而另一种代数为1（这种类型的代数称为常规代数），其中大多数是banach banach banach banach banach banach Alber banach Albras或其他特征。该项目的目的是调查Banach代数，尤其是Banach功能代数的各种条件（包括规律性条件），以相互关联这些条件，并与Banach代数可能满足的其他重要条件相互关联，并研究这些条件可能满足这些条件，并在您形成各种代数的col'Algebraic'Extersions或Extersions（例如Eltemensions ore and extersentions）时，将这些条件均可满足这些条件，并调查这些条件。