Geodesic
On Riesz homomorphisms in unital $f$-algebras
Mathematica Bohemica, Tome 134 (2009) no. 2, pp. 121-131

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 $T\: A\rightarrow A$ a Riesz homomorphism such that $T^2(f)=T(fT(e))$ for all $f\in A$. Then every Riesz homomorphism extension $\widetilde T$ of $T$ from the Dedekind completion $A^{\delta }$ of $A$ into itself satisfies $\widetilde T^2(f)=\widetilde T(fT(e))$ for all $f\in A^{\delta }$. 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.
DOI : 10.21136/MB.2009.140648
Classification : 06F25, 46A40
Keywords: vector lattice; $d$-algebra; $f$-algebra 
@article{10_21136_MB_2009_140648,
     author = {Chil, Elmiloud},
     title = {On {Riesz} homomorphisms in unital $f$-algebras},
     journal = {Mathematica Bohemica},
     pages = {121--131},
     publisher = {mathdoc},
     volume = {134},
     number = {2},
     year = {2009},
     doi = {10.21136/MB.2009.140648},
     mrnumber = {2535141},
     zbl = {1212.06043},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2009.140648/}
}
TY  - JOUR
AU  - Chil, Elmiloud
TI  - On Riesz homomorphisms in unital $f$-algebras
JO  - Mathematica Bohemica
PY  - 2009
SP  - 121
EP  - 131
VL  - 134
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2009.140648/
DO  - 10.21136/MB.2009.140648
LA  - en
ID  - 10_21136_MB_2009_140648
ER  - 
%0 Journal Article
%A Chil, Elmiloud
%T On Riesz homomorphisms in unital $f$-algebras
%J Mathematica Bohemica
%D 2009
%P 121-131
%V 134
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2009.140648/
%R 10.21136/MB.2009.140648
%G en
%F 10_21136_MB_2009_140648
Chil, Elmiloud. On Riesz homomorphisms in unital $f$-algebras. Mathematica Bohemica, Tome 134 (2009) no. 2, pp. 121-131. doi: 10.21136/MB.2009.140648

Cité par Sources :