  We propose an approach to obtaining explicit estimates on the resolvent of
hypocoercive operators by using Schur complements, rather than from an
exponential decay of the evolution semigroup combined with a time integral. We
present applications to Langevin-like dynamics and Fokker--Planck equations, as
well as the linear Boltzmann equation (which is also the generator of
randomized Hybrid Monte Carlo in molecular dynamics). In particular, we make
precise the dependence of the resolvent bounds on the parameters of the
dynamics and on the dimension. We also highlight the relationship of our method
with other hypocoercive approaches.
