Fixed Point Theorems in the Absence of Normal Structure

Abstract

In Chapter VI we studied the f.p.p. as a property which is implied by normal structure. However, there are Banach spaces without normal structure which have the f.p.p. For instance, l^p,∞ does not have normal structure (Example VI.2) but this space has the f.p.p. This fact can be proved, for instance, checking that the Banach-Mazur distance between l^p,∞ and l^p is 2¹/^p and applying a stability result in [By3].