On Asymptotic Structure,the Szlenk Index and UKK Properties in Banach Spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On Asymptotic Structure,the Szlenk Index and UKK Properties in Banach Spaces

Authors:	Knaust H Odell E Schlumprecht Th

Institution:	(1) Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX, 79968-0514, USA, E-mail;(2) Department of Mathematics, University of Texas at Austin, Austin, TX, 78712-1082, USA, E-mail;(3) Department of Mathematics, Texas A&M University, College Station, TX, 77843-3368, USA, E-mail

Abstract:	Let B be a separable Banach space and let X=B ^* be separable. We prove that if B has finite Szlenk index (for all > 0) then B can be renormed to have the weak* uniform Kadec-Klee property. Thus if > 0 there exists () > 0 so that if x _n is a sequence in the ball of X converging ^* to x so that $\lim \inf _{n \to \infty } \left\\| {x_n - x} \right\\| \geqslant \varepsilon {\text{ then }}\left\\| x \right\\| \leqslant 1 - \delta (\varepsilon )$ . In addition we show that the norm can be chosen so that () c^p for some p < and c >0.

Keywords:	asymptotic structure Szlenk index uniform Kadec-Klee property
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