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.
