Mathematical Sciences: Geometry of Banach Spaces and Operator Spaces

数学科学：Banach 空间和算子空间的几何

• 批准号: 9623260
• 负责人: William Johnson
• 金额: $ 37.65万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-06-01 至 2000-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9623260&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometry; Banach; Spaces

9623260 W. B. Johnson and G. Pisier The proposers will investigate problems in the theories of Banach spaces and operator spaces. The problems to be considered involve: local theories of operator spaces and of spaces of measurable functions, polynomially bounded operators, bounded homomorphisms on C* algebras, infinite dimensional linear and nonlinear geometry of Banach spaces. Banach space theory forms the natural framework for studying geometries which are not Euclidean, while the theory of C* algebras is the standard framework for quantum mechanics. Operator spaces are the quantization (in the sense of quantum mechanics) of Banach spaces. This very new theory has already (e.g., in work of Junge and Pisier) had an impact on C* algebras, and part of this work involves approaching other classical problems in C* algebras/operator theory through operator spaces. The nonlinear geometry of Banach spaces is also in a neophyte stage, but work of Bourgain, Gorelik, Johnson-Lindenstrauss-Schechtman, and others suggest that this subject is ready to take-off. There is reason to hope that the nonlinear theory of Banach spaces will have applications in classical nonlinear analysis comparable to the many applications of the linear theory to classical linear analysis.

9623260 W。B. Johnson和G. Pisier将研究巴拿赫空间和算子空间理论中的问题。所考虑的问题包括：算子空间和可测函数空间的局部理论，多项式有界算子，C*代数上的有界同态，无限维Banach空间的线性和非线性几何。巴拿赫空间理论是研究非欧几里得几何的自然框架，而C*代数理论是量子力学的标准框架。算符空间是巴拿赫空间的量子化（在量子力学意义上）。这个非常新的理论已经（例如，在Junge和Pisier的工作中）对C*代数产生了影响，并且这项工作的一部分涉及通过算子空间来解决C*代数/算子理论中的其他经典问题。Banach空间的非线性几何也处于一个新阶段，但Bourgain， Gorelik， Johnson-Lindenstrauss-Schechtman等人的工作表明，这一学科已经准备好起飞。我们有理由希望Banach空间的非线性理论在经典非线性分析中的应用可以与线性理论在经典线性分析中的许多应用相媲美。