Some geometric properties related to smoothness of Banach spaces
type: Item
instance of: scholarly article
title: Some geometric properties related to smoothness of Banach spaces
zbMATH Open document ID: 1109.46018
author: Suyalatu Wulede
author: Alatengsubude Han
author: Laiyou Bao
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2007-01-11T00:00:00Z
review text: We introduce a new class of Banach spaces, locally \(k\) nearly uniformly smooth spaces, which is the dual notion to locally \(k\)-nearly uniformly convex spaces introduced by \textit{D.\,Kutzarova} [J.~Math.\ Anal.\ Appl.\ 162, No.\,2, 322--338 (1991; Zbl 0757.46026)]. The relationships between locally \(k\)-nearly uniformly smooth spaces, locally \(k\)-uniformly smooth Banach spaces, and locally fully \(k\)-smooth Banach spaces are discussed. We also introduce the two new smooth properties, (\(Sk\)-I) and (\(Sk\)-II), which are the extensions of smooth properties (S-I) and (S-II) that were introduced by \textit{Suyalatu} and \textit{X.--M.\ Jin} [J.~Anhui Norm.\ Univ., Nat.\ Sci.\ 22, No.\,1, 13--16 (1999; Zbl 0968.46018)], and discuss the relations between (\(Sk\)-I), (\(Sk\)-II) and other smooth properties. At last, the locally fully \(k\)-smoothness, compact locally fully \(k\)-smoothness, and the smooth properties (\(Sk\)-I) and (\(Sk\)-II) in product space \(l^p(X_i)\) are discussed.
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 5115293
zbMATH Keywords: locally uniformly smooth space
zbMATH Keywords: nearly uniformly smooth space
zbMATH Keywords: locally fully smooth space
zbMATH Keywords: product space
zbMATH Keywords: Banach space
MaRDI profile type: Publication
full work available at URL: j.na.2005.12.012
OpenAlex ID: W2088467013
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DOI: 10.1016/J.NA.2005.12.012
description: scientific article; zbMATH DE number 5115293