A study of the derivation of a known inequality for spectral functions of products of exponentials using the Campbell-Baker-Hausdor formula

Abstract

This paper looks at the study of a derivation of a known inequality for spectral functions of products of exponentials using the Baker - Campbell - Hausdor for- mula. This known inequality is called the Golden-Thompson inequality. The Kalman and the Gramian matrices, Lyapunov equation and matrix exponen- tial, Hadamard's lemma and Duhamel formula as well as the trace inequality due to Araki-Lieb-Thirring are all considered in this work.