Abstract

A CP-semigroup (or quantum dynamical semigroup) is a semigroup φ = {φ_t : t ≥ 0} of normal completely positive linear maps on B(H), H being a separable Hilbert space, which satisfies φ_t(1) = 1 for all t ≥ 0 and is continuous in the time parameter t the natural sense.

Let D be the natural domain of the generator L of φ, φ_t = exptL, t ≥ 0. Since the maps φ_t need not be multiplicative D is typically an operator space, but not an algebra. However, in this note we show that the set of operators

is a *-subalgebra of B(H), indeed A is the largest self-adjoint algebra contained in D. Examples are described for which the domain algebra A is, and is not, strongly dense in B(H).

Authors