Mathematical Sciences: Banach Spaces and Convexity Theory

女性研究机会奖支持 维尔纳教授在巴拿赫空间理论方面的工作。她的一部分 项目涉及的Banach空间的性质，可以是 其特征在于存在适当的重赋范，因为 实例包含同构于 绝对可和序列空间她还将调查 欧几里得空间中凸体的几何学。 Banach空间的理论是关于无限空间中的分析 多维度。对于每个有限维n，只有一个 n维空间，在大多数方面， 一般如在n为1、2或3的熟悉情况中。这些是 用来记录只有一个人的情况， 多个自由度。当自由度的数量 变成了无限的，例如， 一根绳子的配置，有许多可能 合理选择表演的环境空间 分析.一个关键的结构要素，区分这些 一个与另一个的距离是测量距离的方式。 沃纳教授的项目关注的是 以某种方式重新调整距离测量会影响 空间的几何结构。

This Research Opportunities for Women award supports Professor Werner's work in Banach space theory. One part of her project concerns properties of Banach spaces that can be characterized by the existence of appropriate renormings, for instance the property of containing a subspace isomorphic to the space of absolutely summable sequences. She will also investigate the geometry of convex bodies in Euclidean space. The theory of Banach spaces is about analysis in infinitely many dimensions. For each finite dimension n, there is only one n-dimensional space, in most respects as well understood in general as in the familiar cases when n is 1, 2, or 3. These are used to keep track of situations in which there are only finitely many degrees of freedom. When the number of degrees of freedom becomes infinite, as would for instance be necessary to describe the configuration of a piece of string, there are many possible reasonable choices for the ambient space in which to perform analysis. A key element of structure that distinguishes these spaces one from another is the way in which distance is measured. Professor Werner's project is concerned with how the ability to rescale the distance measurement in certain ways impinges on the geometrical structure of the space.