Characterizations of Double Commutant Property on B(H)

Let H be a complex Hilbert space. Denote by B(H) the algebra of all bounded linear operators onH. In this paper, we investigate the non-self-adjoint subalgebras of B(H) 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.