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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Completely positive maps on $ U\sp{\ast} $-algebras


Author: W. L. Paschke
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0300103-9
Keywords: $ ^ \ast $-algebra, $ {B^ \ast }$-algebra, $ {U^\ast}$-algebra, completely positive, positive, $ ^\ast $-representation, unitary
Article copyright: © Copyright 1972 American Mathematical Society