Mathematical Sciences: Problems on the Geometry of Banach Spaces

点击翻译按钮获取中文摘要

This project is mathematical research in Banach space theory. A Banach space is a (usually) infinite-dimensional linear space in which one can take limits in a reasonable way. One reason for the historical development of their theory is that differential equations may be profitably studied from the point of view of operators on certain Banach spaces of functions. Part of the project is to investigate certain aspects of the non- linear geometry of Banach spaces. This is a very new aspect of the theory, which hitherto has concentrated on linear subspaces and linear operators. Another non-linear topic is norm estimates on products of polynomials, wherein the latter are regarded as elements of various natural Banach spaces of functions. The principal investigator will also work on a classical problem for the Banach space of absolutely integrable functions of a real variable.