Exposed operators in \({\mathcal L}(C(X), C(Y))\) (Q1188340)

Summary: A point \(q_ 0\) in a convex set \(Q\) is exposed if there exists a bounded linear functional \(\xi\) such that \(\xi(q_ 0)>\xi(q)\) for all \(q\in Q\setminus\{q_ 0\}\). Characterizations of exposed points of the unit ball and the positive part of the unit ball of \({\mathcal L}(C(X),C(Y))\) are given. We describe the set of strongly exposed points. We also consider exposed operators on \(L^ \infty\)- and \(L^ 1\)-spaces.