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

Montgomery-Smith教授将研究从C(K)到任意Banach空间的算子的余型2常数。这是为了填补已知的余型2如何与C(K)中的算子相关的一个空白，到目前为止，C(K)中的算子只涉及余型2空间中的因式。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领域。它以研究得较好的高斯过程为起点。这项研究是在两个领域的交界处进行的：无限维空间上的概率论和算子论。利用概率的思想研究了算子(无穷维矩阵)的性质，反过来，对这些算子的理解引出了纯概率中的新的有趣的问题。

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.