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arXiv 2001.006962020-01math.FA

On a generalisation of Local Uniform Rotundity

Uday Shankar Chakraborty

备注：: 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)
DOI：: 10.1007/s13226-021-00062-3

英文摘要：

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.

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