# 2-positive almost order zero maps and decomposition rank

## TL;DR

This paper studies 2-positive maps on C*-algebras, providing an internal characterization of almost order zero maps and showing that 2-positivity suffices for defining decomposition rank in certain C*-algebras.

## Contribution

It generalizes Choi's argument to characterize almost order zero maps and reduces the positivity requirement in decomposition rank definitions.

## Key findings

- Characterization of almost order zero maps for 2-positive maps
- Reduction of positivity conditions in decomposition rank
- Extension of multiplicative domain concepts

## Abstract

We consider 2-positive almost order zero (disjointness preserving) maps on C*-algebras. Generalizing the argument of M. Choi for multiplicative domains, we give an internal characterization of almost order zero for 2-positive maps. It is also shown that complete positivity can be reduced to 2-positivity in the definition of decomposition rank for unital separable C*-algebras.