A short proof on lifting of projection properties in Riesz spaces
Wójtowicz, Marek
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999), p. 277-278 / Harvested from Czech Digital Mathematics Library
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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 $T$.

Publié le : 1999-01-01
Classification:  26A99,  46A40,  46B30,  46B40,  46E05 
@article{119083,
     author = {Marek W\'ojtowicz},
     title = {A short proof on lifting of projection properties in Riesz spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {40},
     year = {1999},
     pages = {277-278},
     zbl = {0983.46006},
     mrnumber = {1732648},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119083}
}

Wójtowicz, Marek. A short proof on lifting of projection properties in Riesz spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) pp. 277-278. http://gdmltest.u-ga.fr/item/119083/

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