# Completely bounded isomorphisms of operator algebras and similarity to complete isometries

@article{Clouatre2014CompletelyBI, title={Completely bounded isomorphisms of operator algebras and similarity to complete isometries}, author={Raphael Clouatre}, journal={arXiv: Operator Algebras}, year={2014} }

A well-known theorem of Paulsen says that if $\mathcal{A}$ is a unital operator algebra and $\phi:\mathcal{A}\to B(\mathcal{H})$ is a unital completely bounded homomorphism, then $\phi$ is similar to a completely contractive map $\phi'$. Motivated by classification problems for Hilbert space contractions, we are interested in making the inverse $\phi'^{-1}$ completely contractive as well whenever the map $\phi$ has a completely bounded inverse. We show that there exist invertible operators $X… CONTINUE READING

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