On the numerical index of the real two-dimensional $L_p$ space

TL;DR

This paper calculates the numerical index of two-dimensional real Lp spaces for specific ranges of p, providing precise values that enhance understanding of their geometric properties.

Contribution

It determines the numerical index of 2D real Lp spaces for p in the ranges 6/5 to 3/2 and 3 to 6, which was previously unknown.

Findings

Numerical index computed for 6/5 ≤ p ≤ 3/2

Numerical index computed for 3 ≤ p ≤ 6

Provides exact values for these ranges

Abstract

We compute the numerical index of the two-dimensional real $L_p$ space for $\frac65\leq p\leq \frac32$ and $3\leq p\leq 6$.