Lattice operations of positive bilinear mappings

Abstract

In this paper we establish extension theorems for additive mappings ? : A+ ×B+ ? C+, where A, B are Riesz spaces (lattice ordered spaces or vector lattices) and C is an order complete Riesz space, to the whole of A×B, therebyextendingwell-knownresults for additivemappingsbetween Riesz spaces. We prove, in particular, that when A, B and C are order complete Riesz spaces, the ordered vector space Bb(A × B, C) of all order bounded bilinear mappings has the structure of a lattice space.