Noncommutative Lp-Spaces and Perturbations of KMS States

TL;DR

This paper extends the perturbation theory of KMS states using noncommutative Lp-spaces, establishing stability, analyticity, and bounds for these states under certain unbounded perturbations, with comprehensive background review.

Contribution

It introduces a novel framework for perturbing KMS states with unbounded operators via noncommutative Lp-spaces, enhancing understanding of their stability and analytic properties.

Findings

Established stability of the modular operator domain

Defined and proved analyticity of the multiple-time KMS condition

Provided bounds on the norm of perturbed KMS states

Abstract

We extend the theory of perturbations of KMS states to some class of unbounded perturbations using noncommutative Lp-spaces. We also prove certain stability of the domain of the Modular Operator associated to a ||.||p-continuous state. This allows us to define an analytic multiple-time KMS condition and to obtain its analyticity together with some bounds to its norm. Apart from that, this work contains a detailed review, with minor contributions due to the author, starting with the description of C*-algebras and von Neumann algebras followed by weights and representations, a whole chapter is devoted to the study of KMS states and its physical interpretation as the states of thermal equilibrium, then the Tomita-Takesaki Modular Theory is presented, furthermore, we study analytical properties of the modular operator automorphism group, positive cones and bounded perturbations of states, and finally we start presenting multiple versions of noncommutative Lp-spaces.