Some generalizations of locally uniform rotundity
type: Item
instance of: scholarly article
title: Some generalizations of locally uniform rotundity
zbMATH Open document ID: 0978.46004
author: Pradipta Bandyopadhyay
author: Da Huang
author: S. Troyanski
author: Bor-Luh Lin
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-01-15T00:00:00Z
review text: The authors introduce and study some generalizations of locally uniformly rotund (LUR) norms -- ALUR and WALUR norms. Some characterizations of pointwise versions of these notions are given. Existence of a WALUR norm implies \(\sigma\)-fragmentability of the space but it is not known whether it implies LUR renormability (cf. Question 2 in the paper).
Mathematics Subject Classification ID: 46B03
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46B04
Mathematics Subject Classification ID: 46B26
zbMATH DE Number: 1563099
zbMATH Keywords: weakly almost locally uniformly rotund norm
zbMATH Keywords: rotund point
zbMATH Keywords: \(\sigma\)-fragmentable Banach space
reviewed by: Ondřej F. K. Kalenda
MaRDI profile type: Publication
full work available at URL: jmaa.2000.7169
OpenAlex ID: W2090515955
cites work: Nested sequences of balls, uniqueness of Hahn-Banach extensions and the Vlasov property.
cites work: Smooth bump functions and geomentry of Banach spaces
cites work: Q4186834
cites work: Generic differentiability of convex functions on the dual of a Banach space
cites work: On the Strongly Extreme Points of Convex Bodies in Separable Banach Spaces
cites work: Q4283372
cites work: σ‐fragmentable Banach spaces
cites work: Q4336049
cites work: Fragmentability and Sigma-Fragmentability of Banach Spaces
cites work: Q4938204
cites work: On operators which attain their norm
cites work: Geometry of Banach spaces with \((\alpha,\epsilon)\)-property or \((\beta,\epsilon)\)-property
cites work: Locally uniformly rotund renorming and fragmentability
cites work: On weakly locally uniformly rotund Banach spaces
cites work: Q4882848
cites work: Geometrical properties determined by the higher duals of a Banach space
cites work: Norm attaining operators and renormings of Banach spaces
cites work: APPROXIMATIVE PROPERTIES OF SETS IN NORMED LINEAR SPACES
DOI: 10.1006/JMAA.2000.7169
description: scientific article; zbMATH DE number 1563099