About the Existence of an Isotone Retraction onto a Convex Cone

Sandor Nemeth, AB Nemeth

Research output: Contribution to journalArticle

1 Citation (Scopus)


The existence of continuous isotone retractions onto pointed closed convex cones in Hilbert spaces is studied. The cones admitting such mappings are called isotone retraction cones. In finite dimension, generating, isotone retraction cones are polyhedral. For a closed, pointed, generating cone in a Hilbert space the isotonicity of a retraction and its complement implies that the cone is latticial and the retraction is well defined by the latticial structure. The notion of sharp mapping is introduced. If the cone is generating and normal, it is proved that its latticiality is equivalent to the existence of an isotone retraction onto it, whose complement is sharp. The subdual and autodual latticial cones are also characterized by isotonicity. This is done by attempting to extend Moreau's theorem to retractions.
Original languageEnglish
Pages (from-to)707-720
Number of pages14
JournalJournal of Convex Analysis
Issue number3
Publication statusPublished - 1 Jan 2011


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