The H\"older Inequality for KMS States

TL;DR

This paper establishes a H"older inequality for KMS states, extending classical trace inequalities using the framework of non-commutative Lp spaces, with implications for quantum statistical mechanics.

Contribution

It introduces a generalized H"older inequality for KMS states within the non-commutative Lp space framework, broadening the scope of trace inequalities in quantum theory.

Findings

Proves a new H"older inequality for KMS states.

Extends classical trace inequalities to non-commutative settings.

Utilizes non-commutative Lp space theory to achieve results.

Abstract

We prove a H\"older inequality for KMS States, which generalises a well-known trace-inequality. Our results are based on the theory of non-commutative $L_p$-spaces.