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arXiv · 2104.06827

Logarithmic submajorisations inequalities for operators in a finite von Neumann algebra

Cheng Yan·Yazhou Han
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Abstract

The aim of this paper is to study the logarithmic submajorisations inequalities for operators in a finite von Neumann algebra. Firstly, some logarithmic submajorisations inequalities due to Garg and Aulja are extended to the case of operators in a finite von Neumann algebra. As an application, we get some new Fuglede-Kadison determinant inequalities of operators in that circumstance. Secondly, we improve and generalize to the setting of finite von Neumann algebras, a generalized H\"{o}lder type generalized singular numbers inequality.

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Cheng Yan, Yazhou Han. 2021-04-14. Logarithmic submajorisations inequalities for operators in a finite von Neumann algebra. https://arxiv.org/abs/2104.06827

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