Mathematical Sciences: Problems on the Geometry of Banach Spaces

本课题是关于Banach空间的数学研究 理论 一个Banach空间是一个（通常）无限维的 在线性空间中，人们可以以合理的方式进行限制。 他们理论的历史发展的一个原因是， 微分方程可能是有益的研究，从点 某些Banach函数空间上的算子的观点。 部分 该项目的目的是调查非- Banach空间的线性几何 这是一个非常新的方面， 该理论，迄今已集中在线性子空间 线性算子。 另一个非线性主题是范数估计 关于多项式的乘积，其中后者被视为 各种自然Banach函数空间的元素。 的 首席研究员还将研究一个经典问题， 真实的Banach空间中的绝对可积函数 变量

This project is mathematical research in Banach space theory. A Banach space is a (usually) infinite-dimensional linear space in which one can take limits in a reasonable way. One reason for the historical development of their theory is that differential equations may be profitably studied from the point of view of operators on certain Banach spaces of functions. Part of the project is to investigate certain aspects of the non- linear geometry of Banach spaces. This is a very new aspect of the theory, which hitherto has concentrated on linear subspaces and linear operators. Another non-linear topic is norm estimates on products of polynomials, wherein the latter are regarded as elements of various natural Banach spaces of functions. The principal investigator will also work on a classical problem for the Banach space of absolutely integrable functions of a real variable.