A note on positivity of elementary operators
# A note on positivity of elementary operators

### Richard M. Timoney

## Abstract

We show that operators on n ×n matrices which are
representable in the form T(X) = \sum
_{i = 1}^{l} a_{i} X b_{i} (for
a_{i} and b_{i} n ×n matrices) and are
k-positive for k = [ \sqrt{*l*} ] must be
completely positive.
As a consequence, elementary operators on a C*-algebra with minimal
length *l* which are k-positive for k = [ \sum{*l*} ] must be
completely positive.