Some Classical and Recent Results Concerning Renorming Theory

TL;DR

This paper surveys classical and recent results on renorming Banach spaces, highlighting key problems, findings, and open questions in the field of equivalent norms.

Contribution

It provides a comprehensive overview of both historical and current developments in renorming theory of Banach spaces.

Findings

Summary of classical renorming results

Discussion of recent advances in the field

Identification of open problems in renorming theory

Abstract

The problems connected with equivalent norms lie at the heart of Banach space theory. This is a short survey on some recent as well as classical results and open problems in renormings of Banach spaces.