## Annals of Functional Analysis

- Ann. Funct. Anal.
- Volume 8, Number 2 (2017), 168-176.

### Perspectives and completely positive maps

#### Abstract

We study the filtering of the perspective of a regular operator map of several variables through a completely positive linear map. By this method we are able to extend known operator inequalities of two variables to several variables, with applications in the theory of operator means of several variables. We also extend Lieb and Ruskai’s convexity theorem from two to $n+1$ operator variables for any natural number $n$.

#### Article information

**Source**

Ann. Funct. Anal. Volume 8, Number 2 (2017), 168-176.

**Dates**

Received: 8 August 2016

Accepted: 9 August 2016

First available in Project Euclid: 14 January 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.afa/1484363068

**Digital Object Identifier**

doi:10.1215/20088752-3784269

**Subjects**

Primary: 47A63: Operator inequalities

**Keywords**

partial traces of operator means Lieb and Ruskai’s convexity theorem

#### Citation

Hansen, Frank. Perspectives and completely positive maps. Ann. Funct. Anal. 8 (2017), no. 2, 168--176. doi:10.1215/20088752-3784269. https://projecteuclid.org/euclid.afa/1484363068