A note on bilineer maps on vector lattices

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YILMAZ R.

New Trends in Mathematical Sciences, no.5, pp.168-174, 2017 (Peer-Reviewed Journal)

  • Publication Type: Article / Article
  • Publication Date: 2017
  • Journal Name: New Trends in Mathematical Sciences
  • Journal Indexes: MathSciNet
  • Page Numbers: pp.168-174
  • Recep Tayyip Erdoğan University Affiliated: Yes

Abstract

In this paper we introduce a new concept of a d-bimorphism on a vector lattice and prove that, for vector lattices A and B,the Arens triadjoint T∗∗∗ : (A′)′n ×(A′)′n →(B′)′
n of a d-bimorphism T : A×A→B is a d-bimorphism. This generalizes the concept of
d-algebra and some results on the order bidual of d-algebras.