Journal of Function Spaces (Jan 2021)
Characterizations of Double Commutant Property on BH
Abstract
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.