Exposed and denting points in duals of operator spaces

Abstract

We study the extremal structure of the dual unit balls of various operator spaces. Mainly, we show that the classes of [w*-] strongly exposed, [w*-] exposed, and denting points in the dual unit balls of spaces of compact operators between Banach spaces X and Y are completely - and in a canonical way - determined by the corresponding classes of points in the unit balls of the (bi-)duals of the factor spaces X and Y. Applications to the duality of operator spaces and differentiability properties of the norm in operator spaces are given. © 1986 The Weizmann Science Press of Israel.