Mathematical Sciences: Banach Spaces and Related Topics

本课题是Banach空间理论的数学研究。Dilworth教授计划研究分析中广泛关注的某些Banach空间的线性拓扑性质。其中一些工作涉及勒贝格函数空间和洛伦兹函数空间的无限维子空间结构。还将研究概率问题，如函数空间中独立随机变量和的和的不等式以及函数空间中的鞅差序列的和的不等式。另一个研究方向与指数小于1的勒贝格空间的有限维结构有关。

This project is mathematical research in Banach space theory. Professor Dilworth plans to investigate linear topological properties of certain Banach spaces of broad interest in analysis. Some of this work concerns the infinite-dimensional subspace structure of the Lebesgue and Lorentz function spaces. Probabilistic matters, such as inequalities for sums of independent random variables and of martingale difference sequences in function spaces, will also be investigated. Another research direction has to do with the finite-dimensional structure of the Lebesgue spaces with exponent less than unity.