Geodesic
On some geometric properties of Banach spaces of continuous functions on separable compact lines
Artur Michalak1
1 Faculty of Mathematics and Computer Science A. Mickiewicz University in Poznań Umultowska 87 61-614 Poznań, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 65 (2017) no. 1, pp. 57-68.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We study properties of Banach spaces $C(L)$ of all continuous scalar (real or complex) functions on compact lines $L$. First we show that if $L$ is a separable compact line, then for every closed linear subspace $X$ of $C(L)$ with separable dual the quotient space $C(L)/X$ possesses a sequence of continuous linear functionals separating its points. Next we show that for any compact line $L$ the space $C(L)$ contains no subspace isomorphic to a $C(K)$ space where $K$ is a separable nonmetrizable scattered compact Hausdorff space with countable height.
DOI : 10.4064/ba8086-4-2017
Keywords: study properties banach spaces continuous scalar real complex functions compact lines nbsp first separable compact line every closed linear subspace separable dual quotient space possesses sequence continuous linear functionals separating its points compact line space contains subspace isomorphic space where separable nonmetrizable scattered compact hausdorff space countable height

Artur Michalak 1

1 Faculty of Mathematics and Computer Science A. Mickiewicz University in Poznań Umultowska 87 61-614 Poznań, Poland 
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Artur Michalak. On some geometric properties of Banach spaces of continuous functions on separable compact lines. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 65 (2017) no. 1, pp. 57-68. doi : 10.4064/ba8086-4-2017. http://geodesic.mathdoc.fr/articles/10.4064/ba8086-4-2017/

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