The Arens Triadjoints of some Bilinear Maps


Yilmaz R.

FILOMAT, vol.28, no.5, pp.963-979, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 5
  • Publication Date: 2014
  • Doi Number: 10.2298/fil1405963y
  • Title of Journal : FILOMAT
  • Page Numbers: pp.963-979

Abstract

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].