Isotone retraction cones in Hilbert spaces (Q975848)

Let \(H\) be a Hilbert space and equip \(H\) with the ordering induced by a pointed closed convex cone. So, a mapping on \(H\) is said to be \textit{isotone} if it is monotonically increasing. The notion of sharp mappings is introduced in this note. It is shown then that a pointed closed generating convex cone in \(H\) is latticial if and only if there is a continuous retraction onto the cone with a sharp complement. Particular cases and examples are given throughout. The problem discussed in this note is connected with a series of papers given by the author and Isaac over the last three decades. For more details, the reader is referred to this interesting note and its list of references.