## Completely bounded homomorphisms of operator algebras

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- by Vern I. Paulsen
- Proc. Amer. Math. Soc.
**92**(1984), 225-228 - DOI: https://doi.org/10.1090/S0002-9939-1984-0754708-X
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## 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.## References

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## Bibliographic 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