A note on the computable categoricity of l^p spaces

TL;DR

This paper investigates the conditions under which l^p spaces are computably categorical, establishing that they are so if and only if p is not equal to 2, in both real and complex cases.

Contribution

It provides a complete characterization of the computable categoricity of l^p spaces based on the value of p.

Findings

l^p spaces are computably categorical iff p ≠ 2

The result holds for both real and complex l^p spaces

The case p=2 is characterized by non-computability of categoricity

Abstract

Suppose $p$ is a computable real so that $p \geq 1$. We show that in both the real and complex case $l^p$ is computably categorical if and only if $p \neq 2$.