On geometric constants for discrete Morrey spaces

TL;DR

This paper calculates specific geometric constants for discrete Morrey spaces, revealing their non-uniform convexity properties and contributing to the understanding of their geometric structure.

Contribution

It establishes that the Von Neumann-Jordan and James constants for discrete Morrey spaces are both equal to the space dimension n, a novel result.

Findings

Von Neumann-Jordan constant equals n

James constant equals n

Discrete Morrey spaces are not uniformly non-ell^1

Abstract

In this note we prove that the $n$-th Von Neumann-Jordan constant and the $n$-th James constant for discrete Morrey spaces $\ell^p_q$ where $1\le p<q<\infty$ are both equal to $n$. This result tells us that the discrete Morrey spaces are not uniformly non-$\ell^1$, and hence they are not uniformly $n$-convex.