STRICT CHARACTERIZATION OF COMPLETELY POSITIVE MAPS

N. B. Okelo

Abstract


Let and  be algebras, and   be by  matrices with entries from and  respectively and  be a linear map, then we define maps    by  for all natural numbers . It is known that all completely positive maps are completely bounded maps, however the converse is not necessarily true. In this paper we give an example of a completely positive map that is completely bounded and a counter example.

Keywords: Hermitian maps, Unital -homomorphism, Completely positive maps and Completely bounded maps.


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References


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