On norm derivatives and the ball-covering property of Banach spaces

TL;DR

This paper investigates a local version of the ball-covering problem in Banach spaces, providing a complete solution using norm derivatives and refining existing results through a local approach.

Contribution

It introduces a local approach to the ball-covering problem in Banach spaces and offers a complete solution based on norm derivatives, improving previous results.

Findings

Complete solution to the local ball-covering problem

Refinements of known results using the local approach

Demonstrates advantages of local analysis in Banach space geometry

Abstract

We study a local version of the ball-covering problem in Banach spaces, and obtain a complete solution to it in terms of the norm derivatives. We illustrate the advantage of the local approach by obtaining substantial refinements of several previously known results on this topic.