Extension of Locally Uniform Rotund (LUR) Norm to the Entire Banach Space

Abstract

In this paper, we discuss the extension of norms possessing different rotundity properties from a closed, reflexive, and separable subspace of a Banach space to the entire space. We also explore the possibility of extending an equivalent locally uniform rotund norm from a closed subspace to whole Banach space. In the general setting of Banach spaces, this problem remains unsolved.