Premium
Uniform Boundedness and Closed Graph Theorems for Convex Operators
Author(s) -
Neumann Michael M.
Publication year - 1985
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19851200111
Subject(s) - mathematics , regular polygon , pure mathematics , subderivative , graph , combinatorics , convex optimization , geometry
Abstract We are concerned with convex operators mapping a convex subset of a certain topological vector space into an ordered topological vector space, whose positive cone is assumed to be normal. Under the appropriate topological assumptions, we prove the equicontinuity of every pointwise bounded family of continuous convex operators as well as the continuity of every closed convex operator at every algebraically interior point of the domain. We also show that some weak kind of monotonicity implies the continuity of a convex operator.