STRICT CHARACTERIZATION OF COMPLETELY POSITIVE MAPS
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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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