Positive definite operator sequences

Bisgaard, T.

doi:10.1090/S0002-9939-1994-1197531-3

Positive definite operator sequences
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Proc. Amer. Math. Soc. 121 (1994), 1185-1191 Request permission

Abstract:

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

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Extension of linear transformations in Hilbert space which extend beyond this space