Van Hove Limit for Infinite Systems

We study the van Hove limit for master equations on a Banach space, and propose a contraction semigroup as limit dynamics. The generator has a Lindblad form if specialized to C*-algebras, is always well defined irrespectively of the subsystem spectrum, includes first-order contributions, and returns Davies averaged generator, when the latter is defined. The theory is applied to the case of a free particle in contact with a heat bath.