Mathematical Sciences: Quasi-Banach Spaces and Their Applications

Kalton， Casazza和Montgomery-Smith将继续研究Banach和非局部凸空间的结构，以及它们在其他分析领域的应用，以及概率在Banach空间中的应用。其中要解决的问题是：是否每一个无限维拟巴拿赫空间都有一个合适的闭无限维子空间，如何计算Rademacher级数和的范数的期望值，以及巴拿赫空间对偶中的紧逼近性质是否蕴涵了巴拿赫空间的紧逼近性质。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。

Kalton, Casazza, and Montgomery-Smith will continue their research into the structure of Banach and non-locally convex spaces, and their applications to other areas of analysis, and applications of probability to Banach spaces. Among the questions to be addressed are whether every infinite-dimensional quasi-Banach space has a proper closed infinite-dimensional subspace, how to calculate the expected value of the norm of the sum of a Rademacher series, and whether the compact approximation property in the dual of a Banach space implies the property for the Banach space. 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.