Harnack type inequalities for operators in logarithmic submajorisation

TL;DR

This paper extends Harnack type determinant inequalities and logarithmic submajorisation results to operators within finite von Neumann algebras, broadening their applicability in operator theory.

Contribution

It generalizes existing inequalities to the setting of finite von Neumann algebras, providing new tools for operator analysis.

Findings

Extended Harnack type determinant inequalities to finite von Neumann algebras

Established logarithmic submajorisation inequalities for these operators

Broadened the scope of Fuglede-Kadison determinant inequalities

Abstract

The aim of this paper is to study the Harnack type logarithmic submajorisation and Fuglede-Kadison determinant inequalities for operators in a finite von Neumann algebra. In particular, the Harnack type determinant inequalities due to Lin-Zhang [15] and Yang-Zhang [27] are extended to the case of operators in a finite von Neumann algebra.