caa a22 4500 463245903 CHVBK 20180405153325.0 cr unu---uuuuu 170326e20070701xx s 000 0 eng 10.1007/s00009-007-0111-4 doi (NATIONALLICENCE)springer-10.1007/s00009-007-0111-4 Various Slicing Indices on Banach Spaces [Elektronische Daten] [Petr Hájek, Gilles Lancien] Abstract.: 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(α) spaces, where α is an uncountable ordinal. Finally, we show that if the Szlenk index of a Banach space is ω (first infinite ordinal), then its weak*-dentability index is at most ω2 and that this estimate is optimal. Birkhäuser Verlag Basel/Switzerland, 2007 Szlenk index nationallicence Banach space nationallicence Lavrientiev index nationallicence slicing index nationallicence Hájek Petr Czech Academy of Sciences, Mathematical Institute, AS CR, Žitná, 115 67, Praha 1, Czech Republic aut Lancien Gilles Equipe de Mathématiques UMR 6623, Université de Franche-Comté, 16 route de Gray, 25030, Besançon Cedex, France aut Mediterranean Journal of Mathematics Birkhäuser-Verlag; www.birkhäuser.ch 4/2(2007-07-01), 179-190 1660-5446 4:2<179 2007 4 9 https://doi.org/10.1007/s00009-007-0111-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00009-007-0111-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hájek Petr Czech Academy of Sciences, Mathematical Institute, AS CR, Žitná, 115 67, Praha 1, Czech Republic aut NATIONALLICENCE 700 1- Lancien Gilles Equipe de Mathématiques UMR 6623, Université de Franche-Comté, 16 route de Gray, 25030, Besançon Cedex, France aut NATIONALLICENCE 773 0- Mediterranean Journal of Mathematics Birkhäuser-Verlag; www.birkhäuser.ch 4/2(2007-07-01), 179-190 1660-5446 4:2<179 2007 4 9 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer