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}
}
  • Raphael Clouatre
  • Published 2014
  • Mathematics
  • arXiv: Operator Algebras
  • 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

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 34 REFERENCES
    Abelian, amenable operator algebras are similar to C∗ -algebras
    9
    Nonselfadjoint representations of $C^*$-algebras
    8
    Completely bounded homomorphisms of operator algebras
    35
    Solution of the similarity problem for cyclic representations of C*-algebras
    83
    A polynomially bounded operator on Hilbert space which is not similar to a contraction
    108
    Inner derivations on ultraprime normed real algebras
    7