9501243 Schlumprecht The investigator's proposal contains two parts. The first part discusses some problems in infinite dimensional Banach space theory.The developments in structure theory of Banach spaces over the last four years led to exciting results and new problems.The second part of this proposal treats a Gaussian correlation problem. An old question, rooted in statistics, is to estimate multidimensional confidence regions of (possibly dependent) Gaussian variables. This question can be formulated in a more geometrical language. Namely, whether or not the Gausssian measure of the intersection of two symmetric, convex sets in an n dimensional space is bigger than or equal to the product of their measures. The proposal has two parts. The first part presents a continuation of the proposers work in infinite dimensional Banach space theory, a field in which exciting and astonishing results were achieved in recent years. The second part deals with an old question originating in Statistics. Namely to estimate confidence regions for multidimensional normal distributions from below. ***
