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

Authors

DOI:

https://doi.org/10.3126/ajs.v2i1.87747

Keywords:

Extension, Banach space, Rotund Norm, Locally Uniformly Rotund Norm, Uniformly Rotund Norm.

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.

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Published

2025-12-31

How to Cite

Damai, G. R. (2025). Extension of Locally Uniform Rotund (LUR) Norm to the Entire Banach Space . Api Journal of Science, 2(1), 36–39. https://doi.org/10.3126/ajs.v2i1.87747

Issue

Vol. 2 (2025)

Section

Articles

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