Characterizations of double commutant property on \(\mathscr{B}(\mathscr{H})\) (Q1981851)

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