Extreme operators on function spaces (Q1109314)

Let A, B be Banach algebras and S be a locally compact Hausdorff space. The space of continuous functions from S to A vanishing at infinity is denoted by \(C_ 0(S,A)\). Extreme operators from \(C_ 0(S,A)\) to B are identified in terms of extreme operators from A to B in this paper. The intrinsic differences between extreme operators and nice operators from \(C_ 0(S,A)\) to B are also given. A key role is played by the Arens product in the second dual of a Banach algebra.