Isotone retraction cones in Hilbert spaces
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.
scientific article; zbMATH DE number 5720178
scientific article