Various Slicing Indices on Banach Spaces

0094794 - MÚ 2008 RIV CH eng J - Journal Article
Hájek, Petr Pavel - Lancien, G.
Various Slicing Indices on Banach Spaces.
[Různé ordinární indexy na Banachových prostorech.]
Mediterranean Journal of Mathematics. Roč. 4, č. 1 (2007), s. 179-190. ISSN 1660-5446. E-ISSN 1660-5454
R&D Projects: GA ČR GA201/04/0090
Institutional research plan: CEZ:AV0Z10190503
Keywords : Szlenk index * Banach space * Lavrientiev index
Subject RIV: BA - General Mathematics
Impact factor: 0.414, year: 2007

We give a short and direct proof for the computation of the Szlenk index of the C(K) spaces, when K is a countable compact space and determine their Lavrientiev indices. We also compute the Szlenk index of certain C (.alpha.) spaces, where .alpha. is an uncountable ordinal. Finally, we show that if the Szlenk index of a Banach space is .omega. (first infinite ordinal), then its weak*-dentability index is at most .omega.² and that this estimate is optimal.

Je proveden nový jednoduchý výpočet Szlenkova indexu pro C (.alpha.) prostory.
Permanent Link: http://hdl.handle.net/11104/0154519