Extreme points in duals of complex operator spaces

Abstract

We show that if X X and Y Y are complex Banach spaces, and K ( X , Y ) K(X,Y) is the space of compact linear operators from X X into Y Y , then ext ⁡ B ( K ( X , Y ) ∗ ) = ext ⁡ B ( X ∗ ∗ ) ⊗ ext ⁡ B ( Y ∗ ) \operatorname {ext}B(K{(X,Y)^ * }) = \operatorname {ext}B({X^{ * * }}) \otimes \operatorname {ext}B({Y^ * }) .