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TAIWANESE JOURNAL OF MATHEMATICS, vol.12, no.1, pp.39-49, 2008 (SCI-Expanded)
In this paper we establish extension theorems for additive mappings phi : A(+) x 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 x B, thereby extending well-known results for additive mappings between Riesz spaces. We prove, in particular, that when A, B and C are order complete Riesz spaces, the ordered vector space B-b(A x B,C) of all order bounded bilinear mappings has the structure of a lattice space.