Monotonicity and complex convexity in Banach lattices
type: Item
instance of: scholarly article
title: Monotonicity and complex convexity in Banach lattices
zbMATH Open document ID: 1083.46011
author: Han Ju Lee
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-06-10T00:00:00Z
review text: It is well-known that every complex uniformly convex Banach space has finite cotype, and that the space \(L_1/H_1\) has cotype 2 but cannot be equivalently renormed to be complex uniformly convex. The author shows that in Banach lattices such examples are impossible: every Banach lattice of finite cotype possesses an equivalent complex uniformly convex norm. Unfortunately, by doing this the author just rediscovers a theorem obtained 24 years ago by \textit{E. V. Tokarev} [Funct. Anal. Appl. 15, 150--151 (1981); translation from Funkts. Anal. Prilozh. 15, No. 2, 90--91 (1981; Zbl 0466.46026)]. It is also shown that the complex strict (complex uniform) convexity of a Banach space \(X\) is inherited by vector-valued function spaces \(E(X)\) for those Köthe spaces \(E\) that are complex strictly convex or, respectively, complex uniformly convex.
reviewed by: Vladimir Kadets
Mathematics Subject Classification ID: 46B42
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46B03
zbMATH DE Number: 2174926
zbMATH Keywords: Banach lattice
zbMATH Keywords: cotype
zbMATH Keywords: complex uniform convexity
zbMATH Keywords: spaces of vector-valued functions
Wikidata QID: Q57618304
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.01.017
OpenAlex ID: W2010763372
cites work: Q3683058
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DOI: 10.1016/J.JMAA.2005.01.017
description: scientific article; zbMATH DE number 2174926