On a generalisation of Local Uniform Rotundity
Functional Analysis
2021-06-18 v3
Abstract
In this paper we investigate the property (HLUR), a generalisation of (LUR) property of a Banach space. A Banach space having the property (HLUR) is called an HLUR space. We characterise (HLUR) property with the help of known geometric properties and study various properties of HLUR spaces. We show that for any finite dimensional Banach space, the property (HLUR) coincides with anti-Daugavet property of the space. We also show some applications of HLUR spaces in connection with farthest points of sets.
Keywords
Cite
@article{arxiv.2001.00696,
title = {On a generalisation of Local Uniform Rotundity},
author = {Uday Shankar Chakraborty},
journal= {arXiv preprint arXiv:2001.00696},
year = {2021}
}
Comments
There is a mistake in a proof in page no. 12. This is the reason for the withdrawal of the paper. Indian J Pure Appl Math (2021)