Tytuł pozycji:
On some geometric properties of Banach spaces of continuous functions on separable compact lines
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.
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
