Exposed Operators in $\mathcal B (C(X), C(Y))$

Abstract

A point $q_0$ in a convex set $Q$ is exposed if there exists a bounded linear functional $\xi$ such that $\xi(q_0)$ for all $q \in Q\ \{q_0\}$. Characterizations of exposed points of the unit ball and the positive part of the unit ball of $\mathcal B (C(X), C(Y))$ are given. We describe the set of strongly exposed points. We also consider exposed operators on L^\{infty}- and $L^1$-spaces.