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Start Over Creator Chil, Elmiloud

1. On Riesz homomorphisms in unital f-algebras

Creator:
Chil, Elmiloud
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
vector lattice, d-algebra, and f-algebra
Language:
English
Description:
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(fT(e)) for all f ∈ A. Then every Riesz homomorphism extension Te of T from the Dedekind completion A δ of A into itself satisfies Te2 (f) = Te(fT(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 of the above result is a new approach to the Dedekind completion of commutative d-algebras.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Order bounded orthosymmetric bilinear operator

Creator:
Chil, Elmiloud
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
vector lattice, positive bilinear operator, orthosymmetric bilinear operator, and lattice bimorphism
Language:
English
Description:
It is proved by an order theoretical and purely algebraic method that any order bounded orthosymmetric bilinear operator $b\colon E\times E\rightarrow F$ 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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public