Lattice operations of positive bilinear mappings

Yilmaz R.

TAIWANESE JOURNAL OF MATHEMATICS, vol.12, no.1, pp.39-49, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 1
  • Publication Date: 2008
  • Doi Number: 10.11650/twjm/1500602487
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.39-49
  • Recep Tayyip Erdoğan University Affiliated: Yes


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.