Local uniform convexity and Kadec-Klee type properties in \(K\)-interpolation spaces. I. General theory.
type: Item
instance of: scholarly article
title: Local uniform convexity and Kadec-Klee type properties in \(K\)-interpolation spaces. I. General theory.
zbMATH Open document ID: 1060.46014
DOI: 10.1155/2004/678358
author: P. G. Dodds
author: A. A. Sedaev
author: Theresa K.-Y. Dodds
author: Fedor Sukochev
published in: Journal of Function Spaces and Applications
publication date: 2004-09-28T00:00:00Z
review text: The authors present a systematic study of the interpolation of local uniform convexity and Kadec-Klee type properties in K-interpolation spaces. As a by-product of this study, they show that the theorem of Kadec, namely that each separable Banach space admits an equivalent locally uniformly convex norm, follows directly from their approach (see Corollary 3.6.). Another interesting result is Corollary 5.9: Every locally uniformly convex Banach space with an unconditional basis is isomorphic to a complemented subspace of a locally uniformly convex space with a 1-symmetric basis.
reviewed by: Nicolae Popa
Mathematics Subject Classification ID: 46B70
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46B03
zbMATH DE Number: 2104162
zbMATH Keywords: Banach couple
zbMATH Keywords: K-interpolation space
zbMATH Keywords: local uniform convexity
zbMATH Keywords: Kadec-Klee property.
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2004/678358
OpenAlex ID: W1964310064
description: scientific article; zbMATH DE number 2104162