Mathematical Sciences: Cotype of Operators Between Banach Spaces and Rademacher Processes

数学科学：Banach 空间和 Rademacher 过程之间的算子类型

• 批准号: 9001796
• 负责人: Stephen Montgomery-Smith
• 金额: $ 3.74万
• 依托单位: University of Missouri-Columbia
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-01 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001796&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Cotype; Operators; Between

Professor Montgomery-Smith will conduct research into the study of the cotype 2 constant of operators from C(K) to any Banach space. This is intended to fill a gap on what is already known about how cotype 2 relates to operators from C(K) which has so far dealt only with operators which factor through a space of cotype 2. This research will involve the study of Rademacher processes. This is a recent but very natural area. It takes as its starting point the well studied Gaussian processes. This research is at the interface of two fields: probability and operator theory on infinite dimensional spaces. Properties of operators (infinite dimensional matrices) are studied using ideas from probability and conversely the quest to understand these operators leads to new and interesting questions in pure probability.

Montgomery-Smith教授将进行从C(K)到任意Banach空间的算子的cotype 2常数的研究。 这是为了填补关于 cotype 2 如何与来自 C(K) 的算子相关的已知空白，C(K) 迄今为止仅处理通过 cotype 2 空间进行分解的算子。这项研究将涉及 Rademacher 过程的研究。 这是一个最近但非常自然的区域。 它以经过深入研究的高斯过程为起点。 这项研究处于两个领域的交汇处：无限维空间上的概率论和算子理论。 使用概率的思想来研究算子（无限维矩阵）的属性，相反，理解这些算子的探索会带来纯概率中新的有趣的问题。