2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57919In 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.17 pages, LaTeX. Some references and a result on p-nuclearity for Banach spaces with Schauder basis have been added. Minor changes in version 3 to match the published articleMathematical Physics81T05, 47B10, 47L25text