Displaying similar documents to “Order bounded orthosymmetric bilinear operator”

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...

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.

Finite atomistic lattices that can be represented as lattices of quasivarieties

K. Adaricheva, Wiesław Dziobiak, V. Gorbunov (1993)

Fundamenta Mathematicae

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We prove that a finite atomistic lattice can be represented as a lattice of quasivarieties if and only if it is isomorphic to the lattice of all subsemilattices of a finite semilattice. This settles a conjecture that appeared in the context of [11].

The almost lattice isometric copies of c 0 in Banach lattices

Jinxi Chen (2005)

Commentationes Mathematicae Universitatis Carolinae

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In this paper it is shown that if a Banach lattice E contains a copy of c 0 , then it contains an almost lattice isometric copy of c 0 . The above result is a lattice version of the well-known result of James concerning the almost isometric copies of c 0 in Banach spaces.

Lattice of ℤ-module

Yuichi Futa, Yasunari Shidama (2016)

Formalized Mathematics

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In this article, we formalize the definition of lattice of ℤ-module and its properties in the Mizar system [5].We formally prove that scalar products in lattices are bilinear forms over the field of real numbers ℝ. We also formalize the definitions of positive definite and integral lattices and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [14], and cryptographic systems with lattices [15] and coding...