The Arens Triadjoints of some Bilinear Maps


Yilmaz R.

FILOMAT, cilt.28, ss.963-979, 2014 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 28 Konu: 5
  • Basım Tarihi: 2014
  • Doi Numarası: 10.2298/fil1405963y
  • Dergi Adı: FILOMAT
  • Sayfa Sayıları: ss.963-979

Özet

In this paper we study the Arens triadjoints of some bilinear maps on vector lattices. In particular, we prove that, for Archimedean vector lattices A and B, the Arens triadjoint i) T*** : A '' x A '' -> B '' of a positive orthosymmetric bilinear map T : A x A -> B is positive orthosymmetric, and ii) T*** : A '' x A '' -> A '' of a bi-orthomorphism T : A x A -> A is a bi-orthomorphism. These generalize results on the order bidual of f-algebras and almost f-algebras in [4].