The standard dual of an operator space

Abstract

The notion of a dual of an operator space which is again an operator space has been introduced independently by Vern Paulsen and the author, and by Effros and Ruan. Its significance in the theory of tensor products of operator spaces has already been partially explored by the aforementioned. Here we establish some other fundamental properties of this dual construction, and examine how it interacts with other natural categorical constructs for operator spaces. We define and study a notion of projectivity for operator spaces, and give a noncommutative version of Grothendieck’s characterization of l1 (I) spaces for a discrete set I. © 1992 by Pacific Journal of Mathematics.