Geodesic
A short proof on lifting of projection properties in Riesz spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 2, pp. 277-278 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Let $L$ be an Archimedean Riesz space with a weak order unit $u$. A sufficient condition under which Dedekind [$\sigma$-]completeness of the principal ideal $A_{u}$ can be lifted to $L$ is given (Lemma). This yields a concise proof of two theorems of Luxemburg and Zaanen concerning projection properties of $C(X)$-spaces. Similar results are obtained for the Riesz spaces $B_{n}(T)$, $n=1, 2, \dots$, of all functions of the $n$th Baire class on a metric space $T$.
Let $L$ be an Archimedean Riesz space with a weak order unit $u$. A sufficient condition under which Dedekind [$\sigma$-]completeness of the principal ideal $A_{u}$ can be lifted to $L$ is given (Lemma). This yields a concise proof of two theorems of Luxemburg and Zaanen concerning projection properties of $C(X)$-spaces. Similar results are obtained for the Riesz spaces $B_{n}(T)$, $n=1, 2, \dots$, of all functions of the $n$th Baire class on a metric space $T$.
Classification : 26A99, 46A40, 46B30, 46B40, 46E05
Keywords: Dedekind completeness; spaces of continuous functions; spaces of Baire functions 
@article{CMUC_1999_40_2_a8,
     author = {W\'ojtowicz, Marek},
     title = {A short proof on lifting of projection properties in {Riesz} spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {277--278},
     year = {1999},
     volume = {40},
     number = {2},
     mrnumber = {1732648},
     zbl = {0983.46006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1999_40_2_a8/}
}
TY  - JOUR
AU  - Wójtowicz, Marek
TI  - A short proof on lifting of projection properties in Riesz spaces
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1999
SP  - 277
EP  - 278
VL  - 40
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMUC_1999_40_2_a8/
LA  - en
ID  - CMUC_1999_40_2_a8
ER  - 
%0 Journal Article
%A Wójtowicz, Marek
%T A short proof on lifting of projection properties in Riesz spaces
%J Commentationes Mathematicae Universitatis Carolinae
%D 1999
%P 277-278
%V 40
%N 2
%U http://geodesic.mathdoc.fr/item/CMUC_1999_40_2_a8/
%G en
%F CMUC_1999_40_2_a8
Wójtowicz, Marek. A short proof on lifting of projection properties in Riesz spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 2, pp. 277-278. http://geodesic.mathdoc.fr/item/CMUC_1999_40_2_a8/