Subspaces of L(H) That Are *-Invariant

A result of Choi and Effros says how *-invariant spaces of bounded operators on Hilbert space that contain the identity can be abstractly characterized in terms of their order structure. The aim here is to dispose of the identity and to prove a similar theorem for spaces of bounded operators that are merely *-invariant. Absence of a unit will also permit to deal with duals in a satisfactory way.