## Annals of Functional Analysis

- Ann. Funct. Anal.
- Volume 7, Number 4 (2016), 622-635.

### On the Araki–Lieb–Thirring inequality in the semifinite von Neumann algebra

#### Abstract

This paper extends a recent matrix trace inequality of Bourin–Lee to semifinite von Neumann algebras. This provides a generalization of the Lieb–Thirring-type inequality in von Neumann algebras due to Kosaki. Some new inequalities, even in the matrix case, are also given for the Heinz means.

#### Article information

**Source**

Ann. Funct. Anal., Volume 7, Number 4 (2016), 622-635.

**Dates**

Received: 15 December 2015

Accepted: 5 May 2016

First available in Project Euclid: 23 September 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.afa/1474652186

**Digital Object Identifier**

doi:10.1215/20088752-3660864

**Mathematical Reviews number (MathSciNet)**

MR3550940

**Zentralblatt MATH identifier**

06667758

**Subjects**

Primary: 47A63: Operator inequalities

Secondary: 46L52: Noncommutative function spaces

**Keywords**

Araki–Lieb–Thirring inequality von Neumann algebra $\tau$-measurable operator

#### Citation

Han, Yazhou. On the Araki–Lieb–Thirring inequality in the semifinite von Neumann algebra. Ann. Funct. Anal. 7 (2016), no. 4, 622--635. doi:10.1215/20088752-3660864. https://projecteuclid.org/euclid.afa/1474652186