Completely positive maps on -algebras
Abstract: Completely positive maps on -algebras with identity are characterized in terms of -representations on Hilbert space. A result on restricted multiplicativity of such maps is established, from which it follows that completely positive maps which take unitaries to unitaries are -homomorphisms. It is also shown that positive maps on commutative -algebras with identity are completely positive.
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Keywords: -algebra, -algebra, -algebra, completely positive, positive, -representation, unitary
Article copyright: © Copyright 1972 American Mathematical Society