Mathematical Sciences: Problems in Banach Spaces

Casazza教授将对巴拿赫空间理论中的几个问题进行研究。它们涉及(i)有限维空间中无条件对称结构的唯一性，（ii）近似性质的各种形式，以及（iii）素数Banach空间的存在性。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。但在这里主要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 Casazza will conduct research on several problems in the theory of Banach spaces. They involve (i) uniqueness of unconditional and symmetric structures in finite dimensional spaces, (ii) various forms of the Approximation Property, and (iii) the existence of prime Banach spaces. 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 primarily 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.