On the Auerbach bases of $l^{n}_p$ spaces

TL;DR

This paper classifies Auerbach bases in finite-dimensional l^n_p spaces, providing a complete description especially for l^3_p, enhancing understanding of their geometric structure.

Contribution

It offers a complete classification of Auerbach bases in l^n_p spaces based on basis cardinality, including detailed descriptions for l^3_p.

Findings

Complete classification of Auerbach bases in l^n_p spaces

Explicit description of bases for l^3_p

Simplified understanding for l^2_p

Abstract

In this paper, we study Auerbach basis of the Banach spaces $l^n_p$. We provide a complete classification of the spaces in terms of the cardinality of their bases. We also give a complete description of these bases for $l^3_p$ ($l^2_p$ is easy).