  We introduce a construction of Dirichlet forms on von Neumann algebras M
associated to any eigenvalue of the Araki modular Hamiltonian of a faithful
normal non tracial state, providing also conditions by which the associated
Markovian semigroups are GNS symmetric. The structure of these Dirichlet forms
is described in terms of spatial derivations. Coercivity bounds are proved and
the spectral growth is derived. We introduce a regularizing property of
positivity preserving semigroups (superboundedness) stronger than
hypercontractivity, in terms of the symmetric embedding of M into its standard
space L2(M) and the associated noncommutative Lp(M) spaces. We prove
superboundedness for a special class of positivity preserving semigroups and
that some of them are dominated by the Markovian semigroups associated to the
Dirichlet forms introduced above, for type I factors M. These tools are applied
to a general construction of the quantum Ornstein-Uhlembeck semigroups of the
Canonical Commutation Relations CCR and some of their non-perturbative
deformations.
