Algebra universalis

, Volume 67, Issue 1, pp 29–42 | Cite as

Characterization of hyper-archimedean vector lattices via disjointness preserving bilinear maps

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Abstract

In this paper, we show, among other results, that if A is an archimedean vector lattice, then any orthosymmetric disjointness preserving bilinear map on A × A is order bounded if and only if A is hyper-archimedean.

Finally, we show for a uniformly complete semiprime f-algebra A, that the vector space of all linear operators T from \({\Pi(A) = \{ab; \forall a, b \in A\}}\) into A and the vector space of orthosymmetric bilinear maps \({\Psi: A \times A \rightarrow A}\) are isomorphic if and only if A is hyper-archimedean.

2010 Mathematics Subject Classification

06F25 47B65 

Keywords and phrases

hyper-archimedean disjointness preserving bilinear map f-algebra 
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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Département des Mathématiques, Faculté des Sciences de BizerteUniversité de CarthageZarzounaTunisia

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