Banach algebra homomorphisms and applications

Banach代数同态及其应用

• 批准号: 312585-2011
• 负责人: Ilie, Monica
• 金额: $ 0.73万
• 依托单位: Lakehead University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=571779
• 关键词: Banach; algebra; homomorphisms; applications

The present proposal is in the field of abstract harmonic analysis, a mathematical area concerned with the study of locally compact groups and of the spaces and algebras associated with them. A fundamental question from the early beginnings of the field is to what extent the algebra structure of a given algebra associated to a locally compact group G determines the underlying group G. It is known that the Banach algebra structure completely reflects the structure of G for a series of related algebras such as the group algebra, the measure algebra, as well as their generalizations the Fourier algebra and respectivelly the Fourier-Stieltjes algebra. This is in the sense that two locally compact groups having isometrically isomorphic Banach algebras are necessarily topologically isomorphic. However there are still many open problems if we move away from isometric isomorphisms. We propose to take this line of research in several directions such as investigating the algebra homomorphisms in the new setting of the Figa-Talamanca-Herz algebras and exploring various applications of the description of the completely algebra homomorphisms of the Fourier algebra in terms of piecewise affine maps.

本提案属于抽象调和分析领域，这是一个与局部紧群以及与之相关的空间和代数研究有关的数学领域。 该领域早期的一个基本问题是，与局部紧群 G 相关的给定代数的代数结构在多大程度上决定了底层群 G。众所周知，Banach 代数结构完全反映了 G 的结构系列相关代数，例如群代数、测度代数，以及它们的推广傅里叶代数和傅里叶-斯蒂尔切斯代数。这是指具有等距同构巴纳赫代数的两个局部紧群必然是拓扑同构的。然而，如果我们摆脱等距同构，仍然存在许多悬而未决的问题。 我们建议在几个方向上进行这一研究，例如研究 Figa-Talamanca-Herz 代数新环境中的代数同态，以及探索分段仿射傅立叶代数完全代数同态描述的各种应用地图。