A characterization of square banach spaces

Square Banach spaces are characterized among real Banach spaces in terms of the Alfsen-Effros structure topology on the extreme points of the dual ball. As a corollary, one has that the class of separable square spaces coincides with the class of separableG-spaces. It is also shown that for aG-space (hence for a square space) regularity of the quotient structure topology is equivalent to complete regularity, and that square spaces exist for which this topology is not regular. Part of this paper is from the author’s Ph.D. thesis prepared at Bryn Mawr College under the direction of Professor Frederic Cunningham, Jr., whose valuable guidance is greatly appreciated by the author.