Displaying similar documents to “Contractive projections and Seever’s identity in complex f -algebras”

On algebra homomorphisms in complex almost f -algebras

Abdelmajid Triki (2002)

Commentationes Mathematicae Universitatis Carolinae

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Extensions of order bounded linear operators on an Archimedean vector lattice to its relatively uniform completion are considered and are applied to show that the multiplication in an Archimedean lattice ordered algebra can be extended, in a unique way, to its relatively uniform completion. This is applied to show, among other things, that any order bounded algebra homomorphism on a complex Archimedean almost f -algebra is a lattice homomorphism.

Products in almost f -algebras

Karim Boulabiar (2000)

Commentationes Mathematicae Universitatis Carolinae

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Let A be a uniformly complete almost f -algebra and a natural number p ∈ { 3 , 4 , ⋯ } . Then Π p ( A ) = { a 1 ⋯ a p ; a k ∈ A , k = 1 , ⋯ , p } is a uniformly complete semiprime f -algebra under the ordering and multiplication inherited from A with Σ p ( A ) = { a p ; 0 ≤ a ∈ A } as positive cone.

Order bounded orthosymmetric bilinear operator

Elmiloud Chil (2011)

Czechoslovak Mathematical Journal

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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.

On extensions of orthosymmetric lattice bimorphisms

Mohamed Ali Toumi (2013)

Mathematica Bohemica

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In the paper we prove that every orthosymmetric lattice bilinear map on the cartesian product of a vector lattice with itself can be extended to an orthosymmetric lattice bilinear map on the cartesian product of the Dedekind completion with itself. The main tool used in our proof is the technique associated with extension to a vector subspace generated by adjoining one element. As an application, we prove that if ( A , * ) is a commutative d -algebra and A 𝔡 its Dedekind completion, then, A 𝔡 can...