Mathematical Sciences: The Structure of Banach Spaces

作者将研究有关巴拿赫空间结构的几个问题。Rosenthal和Odell将主要关注无限维问题，而Mascioni将研究有限维空间的定量不变量。Rosenthal和Odell将研究一般非自反空间和某些可分离对偶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。他将研究lp空间的均匀性函数的生长阶数，以及一般空间的对偶生长阶数。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。

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.