Positive definite operator sequences

Abstract

An example is given of a linear mapping from C [ x ] {\mathbf {C}}[x] to M 2 ( C ) {{\mathbf {M}}_2}({\mathbf {C}}) which is positive but not completely positive. It is shown that a positive linear mapping from C [ x ] {\mathbf {C}}[x] to B ( H ) {\mathbf {B}}(\mathcal {H}) is completely positive if certain scalar moment sequences associated with it are determinate.