Mathematical Sciences: Projections on Banach Spaces

Banach空间理论处理无限维现象 在严格的数学框架内。它具有历史意义 与更具体的应用学科的联系，因为， 例如，微分方程的解通常是 很容易被认为是一个适当的Banach 空间在物理学中，人们经常遇到这样的系统： 无限多的自由度，必须在 希尔伯特空间是Banach空间的一种特殊类型。 关于Banach空间有两件有趣的事情， 它（从技术上讲，将其投影到一个补子空间上）， 用有限维的子空间来近似它，在这个子空间中， 可以说是画画和做几何。 校长 这个项目的研究人员将致力于解决一个著名的开放问题 这个问题是关于一个标准的Banach空间的切片 喜欢，并将研究有限维的几何 Banach空间的子空间

Banach space theory treats infinite-dimensional phenomena within the framework of rigorous mathematics. It has historical connections to more concrete applied subjects because, for instance, solutions to differential equations are often conveniently thought of as inhabiting an appropriate Banach space. In physics, one frequently encounters systems with infinitely many degrees of freedom which must be modeled in Hilbert space, a special type of Banach space. Two interesting things to do with a Banach space are to slice it (technically, project it onto a complemented subspace) and to approximate it by finite dimensional subspaces, in which one can so to speak draw pictures and do geometry. The principal investigator for this project will work on a famous open problem that asks what the slices of a certain standard Banach space look like, and will investigate the geometry of finite-dimensional subspaces of Banach spaces.