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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Completely bounded homomorphisms of operator algebras
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by Vern I. Paulsen PDF
Proc. Amer. Math. Soc. 92 (1984), 225-228 Request permission

Abstract:

Let $A$ be a unital operator algebra. We prove that if $\rho$ is a completely bounded, unital homomorphism of $A$ into the algebra of bounded operators on a Hilbert space, then there exists a similarity $S$, with $\left \| {{S^{ - 1}}} \right \| \cdot \left \| S \right \| = {\left \| \rho \right \|_{cb}}$, such that ${S^{ - 1}}\rho ( \cdot )S$ is a completely contractive homomorphism. We also show how Rota’s theorem on operators similar to contractions and the result of Sz.-Nagy and Foias on the similarity of $\rho$-dilations to contractions can be deduced from this result.
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 92 (1984), 225-228
  • MSC: Primary 47D25; Secondary 46L05
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0754708-X
  • MathSciNet review: 754708