# p-Nuclearity in a New Perspective

December 09, 2004

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.

Keywords:

phase space conditions, quantum energy inequalities