On some geometric properties of Banach spaces of continuous functions on separable compact lines

• Autorzy: Michalak A.

Identyfikatory

DOI

10.4064/ba8086-4-2017

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

compact lines; Banach spaces of continuous functions

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2017
• Tom: Vol. 65, no. 1
• Strony: 57--68
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Michalak A.

• Faculty of Mathematics and Computer Science, A. Mickiewicz University in Poznań, Umultowska 87, 61-614 Poznań, Poland

Bibliografia

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Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).