Geodesic
On the Arens Homomorphism
Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 2, pp. 82-91

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $E$ be a unital $f$-module over an $f$-algebra $A$. With the help of Arens extension theory, a $(A^{\sim})_{n}^{\sim}$ module structure on $E^{\sim}$ can be defined. The paper deals mainly with properties of the Arens homomorphism $\eta\colon(A^{\sim})_{n}^{\sim}\to \operatorname{Orth}(E^{\sim})$, which is defined by the $(A^{\sim})_{n}^{\sim}$ module structure on $E^{\sim}$. Necessary and sufficient conditions for an $A$ submodule of $E$ to be an order ideal are obtained.
Keywords: Riesz space, orthomorphism
Mots-clés : $f$-module, Arens homomorphism. 
@article{FAA_2022_56_2_a7,
     author = {B. Turan and M. Aslanta\c{s}},
     title = {On the {Arens} {Homomorphism}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {82--91},
     publisher = {mathdoc},
     volume = {56},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2022_56_2_a7/}
}
TY  - JOUR
AU  - B. Turan
AU  - M. Aslantaş
TI  - On the Arens Homomorphism
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2022
SP  - 82
EP  - 91
VL  - 56
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2022_56_2_a7/
LA  - ru
ID  - FAA_2022_56_2_a7
ER  - 
%0 Journal Article
%A B. Turan
%A M. Aslantaş
%T On the Arens Homomorphism
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2022
%P 82-91
%V 56
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2022_56_2_a7/
%G ru
%F FAA_2022_56_2_a7
B. Turan; M. Aslantaş. On the Arens Homomorphism. Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 2, pp. 82-91. http://geodesic.mathdoc.fr/item/FAA_2022_56_2_a7/