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The Szlenk index of L p ( X )
Author(s) -
Hájek Petr,
Schlumprecht Thomas
Publication year - 2014
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdt106
Subject(s) - mathematics , index (typography) , statistics , computer science , world wide web
We find an optimal upper bound on the values of the weak∗ ‐dentability index Dz ( X ) in terms of the Szlenk index Sz ( X ) of a Banach space X with separable dual. Namely, if Sz ( X ) = ω α , for some α < ω 1 , and p ∈ ( 1 , ∞ ) , thenSz ( X ) ⩽ Dz ( X ) ⩽ Sz ( L p ( X ) ) ⩽ω α + 1ifαis a finite ordinal ,ω αifαis an infinite ordinal .