Mathematical Sciences: Geometry and Numerical Characteristics of Banach Spaces

数学科学：Banach 空间的几何和数值特征

• 批准号: 8701041
• 负责人: Daniel Lewis
• 金额: $ 2万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1988-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701041&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometry; Numerical; Characteristics

Banach space theory is a basic tool of mathematical analysis that has been of importance since its inception at the turn of the century. It has increasingly more significant rapport with, and important applications to, various areas of modern analysis and probability theory. World centers of excellence in this area are in Israel, Paris, Warsaw, Ohio, and Texas. Professor Lewis is an expert in the internal structure theory and geometry of Banach spaces. He has been one of the important contributors to the computation of parameters of finite dimensional spaces, and his work has influenced substantially the development of Banach space theory. Professor Lewis will continue his investigations into the geometry of Banach spaces through a study of the numerical characteristics of the spaces and the applications to qualitative properties of spaces and operators. He will consider relative and absolute projection constants, exact values of projection parameters, and invertibility of linear maps.

Banach空间理论是数学分析的基本工具 自1999年开始以来， 世纪。 它与以下方面的关系越来越密切， 以及现代分析的各个领域的重要应用 和概率论。 该领域的世界卓越中心 在以色列、巴黎、华沙、俄亥俄州和德克萨斯州。 刘易斯教授是内部结构方面的专家 Banach空间的理论和几何。 他一直是 重要贡献者的参数计算有限 他的工作对世界的影响很大， Banach空间理论的发展。 刘易斯教授将 继续他对Banach空间几何的研究 通过研究空间的数值特征， 以及在空间定性性质上的应用， 运营商 他将考虑相对和绝对投影 常量、投影参数的精确值，以及 线性映射的可逆性