  We investigate the possibility to suppress interactions between a finite
dimensional system and an infinite dimensional environment through a fast
sequence of unitary kicks on the finite dimensional system. This method, called
dynamical decoupling, is known to work for bounded interactions, but physical
environments such as bosonic heat baths are usually modelled with unbounded
interactions, whence here we initiate a systematic study of dynamical
decoupling for unbounded operators. We develop a sufficient decoupling
criterion for arbitrary Hamiltonians and a necessary decoupling criterion for
semibounded Hamiltonians. We give examples for unbounded Hamiltonians where
decoupling works and the limiting evolution as well as the convergence speed
can be explicitly computed. We show that decoupling does not always work for
unbounded interactions and provide both physically and mathematically motivated
examples.
