Differentiability and ball-covering property in Banach spaces
type: Item
instance of: scholarly article
title: Differentiability and ball-covering property in Banach spaces
zbMATH Open document ID: 1332.46021
author: Shaoqiang Shang
published in: Journal of Mathematical Analysis and Applications
publication date: 2015-11-10T00:00:00Z
review text: A real Banach space is defined to have the ball-covering property if its unit sphere is contained in the union of countably many open balls that do not contain the origin. The main result of the paper is: The following two statements are equivalent for two Gâteaux differentiability spaces \(X\) and \(Y\): (1)~\(X\) and \(Y\) have the ball covering property. (2)~For some \(p\in [1,\infty]\), the product space (\(X\times Y, \|.\|_p)\) has the ball-covering property. (3)~For all \(p\in [1,\infty]\), the product space (\(X\times Y, \|.\|_p)\) has the ball-covering property.
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46G05
zbMATH DE Number: 6506796
zbMATH Keywords: convex function
zbMATH Keywords: Gâteaux differentiability space
zbMATH Keywords: ball-covering property
reviewed by: Srinivasa Swaminathan
MaRDI profile type: Publication
full work available at URL: j.jmaa.2015.09.009
OpenAlex ID: W1852283239
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DOI: 10.1016/J.JMAA.2015.09.009
description: scientific article; zbMATH DE number 6506796