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.