Mathematical Sciences: The Structure of Banach Spaces

提出者将研究与Banach空间结构有关的几个问题。罗森塔尔和奥德尔将主要关注无限维问题，而马西奥尼将研究有限维空间的量化不变量。Rosenthal和Odell将研究一般非自反空间和某些具有可分对偶的空间的商的子空间结构。Mascioni将研究与一致逼近性质有关的不变量。他将与UAP一起研究Lp-空间的一致函数的增长级，以及一般空间的对偶级增长。Banach空间理论是试图将三维欧几里得(即普通)空间的结构推广到无限多维的数学部分。Banach空间中距离函数的公理比欧几里德距离的公理要宽松得多(例如，不需要遵守“平行四边形定律”)，因此，Banach空间的“几何”可能是相当奇异的。这方面的许多研究都涉及到对Banach空间的结构理论的研究。

The proposers will study several problems concerning the structure of Banach spaces. Rosenthal and Odell will focus mainly on infinite-dimensional issues, while Mascioni will study quantitative invariants for finite-dimensional spaces. Rosenthal and Odell will work on the subspace structure of general non- reflexive spaces and of quotients of certain spaces with separable duals. Mascioni will study invariants connected with the uniform approximation property. He will investigate the order of growth of the uniformity function of Lp-spaces, and the duality-order of growth of general spaces with the uap. 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.