Completely positive maps on $U^{\ast }$-algebras
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- by W. L. Paschke PDF
- Proc. Amer. Math. Soc. 34 (1972), 412-416 Request permission
Abstract:
Completely positive maps on ${U^ \ast }$-algebras with identity are characterized in terms of $^ \ast$-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 $^ \ast$-homomorphisms. It is also shown that positive maps on commutative ${U^ \ast }$-algebras with identity are completely positive.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 34 (1972), 412-416
- MSC: Primary 46K99
- DOI: https://doi.org/10.1090/S0002-9939-1972-0300103-9
- MathSciNet review: 0300103