Abelian, amenable operator algebras are similar to C∗ -algebras

@article{Marcoux2016AbelianAO,
  title={Abelian, amenable operator algebras are similar to C∗ -algebras},
  author={L. Marcoux and A. I. Popov},
  journal={Duke Mathematical Journal},
  year={2016},
  volume={165},
  pages={2391-2406}
}
Suppose that H is a complex Hilbert space and that B(H) denotes the bounded linear operators on H. We show that every abelian, amenable operator algebra is similar to a C*-algebra. We do this by showing that if A is an abelian subalgebra of B(H) with the property that given any bounded representation $\varrho: A \to B(H_\varrho)$ of A on a Hilbert space $H_\varrho$, every invariant subspace of $\varrho(A)$ is topologically complemented by another invariant subspace of $\varrho(A)$, then A is… Expand
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