Mathematical Sciences: Structure Theory of Infinite Dimensional Banach Spaces

Schlumprecht将继续研究Banach空间的结构理论和局部理论，特别是畸变问题。Schlumprecht最近在这一领域的工作对解决几个长期存在的问题做出了重大贡献，包括无条件基问题，超平面问题和素数巴拿赫空间问题，并将在这些和相关领域取得更多成果。巴拿赫空间理论是数学的一部分，它试图将三维欧几里得空间（即普通空间）的结构推广到无限多维。巴拿赫空间中距离函数的公理比欧几里得距离的公理更宽松（例如，“平行四边形定律”不需要成立），因此，巴拿赫空间的“几何”可能相当奇特。该领域的研究主要集中在Banach空间的结构理论研究上。

Schlumprecht will continue his study of the structure theory and local theory of Banach spaces, and specifically, the distortion problem. Schlumprecht's recent work in this area contributed significantly to the solutions of several long standing problems, including the unconditional basis problem, the hyperplane problem, and the prime Banach space problem, and additional results in these and related areas will be pursued. Banach space theory is that part of mathematics that attempts to generalize to infinitely many dimensions the structure of 3-dimensional Euclidean (i.e.ordinary) space. The axioms for the distance function in a Banach space are more relaxed than those for Euclidean distance (For example, the "parallelogram law" is not required to hold.), and as a result, the "geometry" of a Banach space can be quite exotic. Much of the research in this area concerns studying the structure theory of Banach spaces.