p-Nuclearity in a New Perspective

2004/12/31 by Christopher J. Fewster, Izumi Ojima, Izumi ojima +1 · 1 citation
Mathematics · Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #Statistical Mechanics and Entropy #math-ph #math.MP #msc:47B10 #msc:47L25 #msc:81T05

paper · pdf · doi:10.1007/s11005-005-8445-y

published as Lett. Math. Phys. 73 (2005) 1-15 · 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 article

openalex publication_date 2005/07/01 · arxiv created 2005/09/02 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

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