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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Induced representations of $ C\sp{\ast} $-algebras and complete positivity


Author: James G. Bennett
Journal: Trans. Amer. Math. Soc. 243 (1978), 1-36
MSC: Primary 46L05; Secondary 15A63, 43A35
MathSciNet review: 502890
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Abstract: It is shown that $ ^{*}$representations may be induced from one $ {C^{\ast}}$-algebra B to another $ {C^{\ast}}$-algebra A via a vector space equipped with a completely positive B-valued inner product and a $ ^{*}$representation of A. Theorems are proved on induction in stages, on continuity of the inducing process and on completely positive linear maps of finite dimensional $ {C^{\ast}}$-algebras and of group algebras.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0502890-3
PII: S 0002-9947(1978)0502890-3
Article copyright: © Copyright 1978 American Mathematical Society