Lattice operations of positive bilinear mappings

Yilmaz R.

TAIWANESE JOURNAL OF MATHEMATICS, cilt.12, sa.1, ss.39-49, 2008 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 1
  • Basım Tarihi: 2008
  • Doi Numarası: 10.11650/twjm/1500602487
  • Dergi Adı: TAIWANESE JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.39-49
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Evet

Özet

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.