- Tytuł:
- Valdivia compacta and equivalent norms
- Autorzy:
- Kalenda, Ondřej
- Powiązania:
- https://bibliotekanauki.pl/articles/1206143.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Corson compact space
Valdivia compact space
projectional resolution of the identity
countably 1-norming Markushevich basis
equivalent norm - Opis:
- We prove that the dual unit ball of a Banach space X is a Corson compactum provided that the dual unit ball with respect to every equivalent norm on X is a Valdivia compactum. As a corollary we show that the dual unit ball of a Banach space X of density $ℵ_1$ is Corson if (and only if) X has a projectional resolution of the identity with respect to every equivalent norm. These results answer questions asked by M. Fabian, G. Godefroy and V. Zizler and yield a converse to Amir-Lindenstrauss' theorem.
- Źródło:
-
Studia Mathematica; 2000, 138, 2; 179-191
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł