Mathematical Sciences: Structures and Applications of JB*Triples

数学科学：JB*三元组的结构和应用

• 批准号: 8805256
• 负责人: Bernard Russo
• 金额: $ 13.38万
• 依托单位: University of California-Irvine
• 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: 1988-07-01 至 1992-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8805256&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Structures; Applications; JB

This project is mathematical research on a class of objects, known as Banach Jordan triple systems or JB*-triples, that are Banach spaces equipped with a compatible ternary product satisfying certain algebraic conditions. Their study thus incorporates geometry in infinitely many dimensions, and a species of nonassociative algebra. As the use of Jordan's name suggests, these structures have applications in mathematical physics and the foundations of quantum mechanics. Strictly within mathematics, many useful consequences can be extracted once one knows that a given convex set is in fact the unit ball of a JB*-triple. One specific objective of the research is to characterize geometrically the Banach spaces that are duals of JB*-triples. Derivations, bounded and unbounded, of JB*-triples will also be studied. Finally, the manifold consequences of changing the underlying field of scalars from the complex numbers to the real numbers will be explored.

这个项目是关于一类对象的数学研究，称为Banach Jordan三元系或JB*-三元组，它们是配备了满足某些代数条件的相容三进制积的Banach空间。因此，他们的研究包含了无限多个维度的几何学，以及一种非结合代数。正如乔丹名字的用法所暗示的那样，这些结构在数学物理和量子力学的基础上都有应用。在严格的数学范围内，一旦知道给定的凸集实际上是JB*-三元组的单位球，就可以提取出许多有用的结果。研究的一个具体目标是对JB*-三元组的对偶的Banach空间进行几何刻画。还将研究JB*-三元组的有界和无界导子。最后，我们将探讨将标量的基本场从复数改为实数的多种结果。