  We study the potential theory of a large class of infinite dimensional L\'evy
processes, including Brownian motion on abstract Wiener spaces. The key result
is the construction of compact Lyapunov functions, i.e. excessive functions
with compact level sets. Then many techniques from classical potential theory
carry over to this infinite dimensional setting. Thus a number of potential
theoretic properties and principles can be proved, answering long standing open
problems even for the Brownian motion on abstract Wiener space, as e.g.
formulated by R. Carmona in 1980. In particular, we prove the analog of the
known result, that the Cameron-Martin space is polar, in the L\'evy case and
apply the technique of controlled convergence to solve the Dirichlet problem
with general (not necessarily continuous) boundary data.
