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
Cet article a éte moissonné depuis 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.
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
Affiliations des auteurs :
Artur Michalak 1
@article{10_4064_ba8086_4_2017,
author = {Artur Michalak},
title = {On some geometric properties of {Banach} spaces of continuous functions on separable compact lines},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
pages = {57--68},
year = {2017},
volume = {65},
number = {1},
doi = {10.4064/ba8086-4-2017},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ba8086-4-2017/}
}
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%0 Journal Article %A Artur Michalak %T On some geometric properties of Banach spaces of continuous functions on separable compact lines %J Bulletin of the Polish Academy of Sciences. Mathematics %D 2017 %P 57-68 %V 65 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4064/ba8086-4-2017/ %R 10.4064/ba8086-4-2017 %G en %F 10_4064_ba8086_4_2017
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
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