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On Riesz homomorphisms in unital f -algebras

Elmiloud Chil — 2009

Mathematica Bohemica

The main topic of the first section of this paper is the following theorem: let A be an Archimedean f -algebra with unit element e , and T A A a Riesz homomorphism such that T 2 ( f ) = T ( f T ( e ) ) for all f A . Then every Riesz homomorphism extension T ˜ of T from the Dedekind completion A δ of A into itself satisfies T ˜ 2 ( f ) = T ˜ ( f T ( e ) ) for all f A δ . In the second section this result is applied in several directions. As a first application it is applied to show a result about extensions of positive projections to the Dedekind completion. A second application...

Order bounded orthosymmetric bilinear operator

Elmiloud Chil — 2011

Czechoslovak Mathematical Journal

It is proved by an order theoretical and purely algebraic method that any order bounded orthosymmetric bilinear operator b : E × E F where E and F are Archimedean vector lattices is symmetric. This leads to a new and short proof of the commutativity of Archimedean almost f -algebras.

Orthosymmetric bilinear map on Riesz spaces

Elmiloud ChilMohamed MokaddemBourokba Hassen — 2015

Commentationes Mathematicae Universitatis Carolinae

Let E be a Riesz space, F a Hausdorff topological vector space (t.v.s.). We prove, under a certain separation condition, that any orthosymmetric bilinear map T : E × E F is automatically symmetric. This generalizes in certain way an earlier result by F. Ben Amor [On orthosymmetric bilinear maps, Positivity 14 (2010), 123–134]. As an application, we show that under a certain separation condition, any orthogonally additive homogeneous polynomial P : E F is linearly represented. This fits in the type of results by...

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