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

Montgomery-Smith教授将对C(K)到任何巴拿赫空间的算子的共型2常数进行研究。这是为了填补已知的关于cotype 2如何与C(K)中的算子相关的空白，到目前为止，C(K)只处理通过cotype 2空间因子的算子。本研究将涉及Rademacher过程的研究。这是最近才出现的，但很自然。它以研究得很好的高斯过程作为起点。本研究是无限维空间上的概率论和算子论两个领域的交叉点。算子（无限维矩阵）的性质是用概率论的思想来研究的，反过来，理解这些算子的探索会导致纯概率论中新的和有趣的问题。

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.