Mathematical Sciences: Banach Spaces, Operators and Related Topics

Szarek教授将研究Banach空间的同构理论，有限维算子理论中的一些问题，以及与这些领域相关的科学计算。要研究的问题之一是是否存在极端刚性的无限维巴拿赫空间，例如Calkin代数是阿贝尔的或仅由单位算子的倍数组成。该奖项将支持巴拿赫空间的几何研究。在有限维空间中，所有的向量空间本质上是相同的。但是在我们感兴趣的无限维情况下，情况远非如此。巴拿赫空间是无限维空间，空间中点间距离的不同概念引入了额外的结构。这种空间在数学中有广泛的应用，无论是纯粹的还是应用的。

Professor Szarek will study the isomorphic theory of Banach spaces, some problems from finite dimensional operator theory, and scientific computation linked to these areas. One of the problems to be investigated is whether extremely rigid infinite dimensional Banach spaces exist where for example the Calkin algebra is abelian or consists only of multiples of the identity operator. This award will support research in the geometry of Banach spaces. In finite dimensions, all vector spaces are essentially the same. But in the infinite dimensional situation of interest here, this is far from the case. Banach spaces are infinite dimensional spaces with the additional structure introduced by varying notions of distance between points in the space. Such spaces have wide application in mathematics, both pure and applied.