Journal of Function Spaces (Jan 2021)

Characterizations of Double Commutant Property on BH

  • Chaoqun Chen,
  • Fangyan Lu,
  • Cuimei Cui,
  • Ling Wang

DOI
https://doi.org/10.1155/2021/6654100
Journal volume & issue
Vol. 2021

Abstract

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Let H be a complex Hilbert space. Denote by BH the algebra of all bounded linear operators on H. In this paper, we investigate the non-self-adjoint subalgebras of BH of the form T+B, where B is a block-closed bimodule over a masa and T is a subalgebra of the masa. We establish a sufficient and necessary condition such that the subalgebras of the form T+B has the double commutant property in some particular cases.