Non-linear traces on matrix algebras, majorization, unitary invariant norms and 2-positivity

TL;DR

This paper explores non-linear traces on matrix algebras, revealing their partial additivity properties and connections to majorization, unitary invariant norms, and 2-positivity, thus advancing the understanding of non-linear functional analysis in matrix theory.

Contribution

It characterizes non-linear traces of Choquet and Sugeno types through their partial additivities and establishes their relationships with majorization, unitary invariant norms, and 2-positivity.

Findings

Partial additivities characterize non-linear traces of Choquet and Sugeno types.

Connections established between non-linear traces, majorization, and unitary invariant norms.

Insights into 2-positivity related to non-linear traces on matrix algebras.

Abstract

We study non-linear traces of Choquet type and Sugeno type on matrix algebras. They have certain partial additivities. We show that these partial additivities characterize non-linear traces of both Choquet type and Sugeno type respectively. There exists a close relation among non-linear traces of Choquet type, majorization, unitary invariant norms and 2-positivity.