  We prove the quantum Zeno effect in open quantum systems whose evolution,
governed by quantum dynamical semigroups, is repeatedly and frequently
interrupted by the action of a quantum operation. For the case of a quantum
dynamical semigroup with a bounded generator, our analysis leads to a
refinement of existing results and extends them to a larger class of quantum
operations. We also prove the existence of a novel strong quantum Zeno limit
for quantum operations for which a certain spectral gap assumption, which all
previous results relied on, is lifted. The quantum operations are instead
required to satisfy a weaker property of strong power-convergence. In addition,
we establish, for the first time, the existence of a quantum Zeno limit for the
case of unbounded generators. We also provide a variety of physically
interesting examples of quantum operations to which our results apply.
