Banach space theory is a basic tool of mathematical analysis that has been of importance since its inception at the turn of the century. It has increasingly more significant rapport with, and important applications to, various areas of modern analysis and probability theory. World centers of excellence in this area are in Israel, Paris, Warsaw, Ohio, and Texas. Professor Lewis is an expert in the internal structure theory and geometry of Banach spaces. He has been one of the important contributors to the computation of parameters of finite dimensional spaces, and his work has influenced substantially the development of Banach space theory. Professor Lewis will continue his investigations into the geometry of Banach spaces through a study of the numerical characteristics of the spaces and the applications to qualitative properties of spaces and operators. He will consider relative and absolute projection constants, exact values of projection parameters, and invertibility of linear maps.
