Relative annihilators and relative commutants in non-selfadjoint operator algebras

  title={Relative annihilators and relative commutants in non-selfadjoint operator algebras},
  author={L. Marcoux and A. Sourour},
  journal={J. Lond. Math. Soc.},
  • L. Marcoux, A. Sourour
  • Published 2012
  • Mathematics, Computer Science
  • J. Lond. Math. Soc.
  • We extend von Neumann’s Double Commutant Theorem to the setting of nonselfadjoint operator algebras A, while restricting the notion of commutants of a subset S of A to those operators in A which commute with every operator in S. If A is a completely distributive commutative subspace lattice algebra acting on a Hilbert space H, we obtain an alternate characterization (to those of Erdos–Power and of Deguang) of the weak operator closed ideals of A. In the case of nest algebras, we use this… CONTINUE READING
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