Mathematical Sciences: Geometry of Classical Banach Spaces and Convex Bodies

点击翻译按钮获取中文摘要

Alspach will investigate the preduals of the space of absolutely summable sequences and their relation to the spaces of continuous functions. In particular, questions such as which of these preduals are quotients of a space of continuous functions with separable dual are to be considered. Schutt will continue his investigation of the floating body of a convex body and extend the investigations to random polytopes and their relation to polyhedral approximation and the hyperplane problem. 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.