p-Nuclearity in a New Perspective

TL;DR

This paper clarifies misconceptions about p-nuclearity, showing the nuclearity index vanishes for p > 1, and proposes a new perspective linking phase space criteria and quantum energy inequalities.

Contribution

It introduces a novel perspective on p-nuclearity using epsilon-entropy and operator spaces, addressing confusion in existing literature.

Findings

Nuclearity index vanishes for p > 1 in physics literature

Proposes a new framework connecting phase space criteria and quantum inequalities

Clarifies misconceptions about p-nuclearity usage

Abstract

In this paper we try to settle some confused points concerning the use of the notion of p-nuclearity in the mathematical and physical literature, pointing out that the nuclearity index in the physicists' sense vanishes for any p > 1. Our discussion of these issues suggests a new perspective, in terms of epsilon-entropy and operator spaces, which might permit connections to be drawn between phase space criteria and quantum energy inequalities.