Mathematical Sciences: Structures and Applications of JB*Triples

这个项目是对一类物体的数学研究， 称为巴拿赫约旦三元系或JB*-三元系， 具有相容三元积的Banach空间 满足一定的代数条件。 因此，他们的研究 在无限多个维度上融合了几何学， 非结合代数的一种。 使用乔丹的名字 这些结构在数学上有应用 物理学和量子力学的基础。 严格 在数学中，可以提取出许多有用的结果， 一旦知道给定的凸集实际上是单位球， 一个JB*-三倍。 研究的一个具体目标是描述 几何上的Banach空间是JB*-三元组的乘积。 JB*-三元组的有界和无界导数也将是 研究了最后，改变世界的多方面后果 从复数到真实的标量的基础域 数字将被探索。

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.