Mathematical Sciences: Structure Theory of Infinite Dimensional Banach Spaces

Schlumprecht将继续他对结构理论的研究 和Banach空间的局部理论，特别是， 失真问题。 Schlumprecht最近在这方面的工作 为解决几个长期的 长期存在的问题，包括无条件基础问题， 超平面问题，以及Banach空间问题， 将在这些领域和相关领域取得更多成果。 Banach空间理论是数学的一部分， 试图将其推广到无限多个维度， 三维欧氏空间的结构。 的 Banach空间中距离函数的公理更多 比欧几里得距离的那些更宽松（例如， “法律”不需要持有。），且结果， 巴拿赫空间的“几何学”可以是相当奇异的。 大部分 这方面的研究涉及到结构理论的研究 Banach空间。

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.