We show that semigroups of endomorphisms of B(H) can often be associated with a dynamical principle; that is, an infinitesimal structure that completely determines the dynamics. These dynamical invariants are similar to the second order differential equations of classical mechanics, in that one can locate a space of momentum operators, a “Riemannian metric”, and a potential. In the simplest cas...

We prove that in a large class of Banach spaces analytic functions the unit disc ⅅ an (unbounded) operator Af = G · f′ + g f with G, generates C0-semigroup weighted composition operators if and only it C0-semigroup. Particular instances such are classical Hardy spaces. Our result generalizes previous results this context is related to cocycles flows on Likewise, for non-separable X contained Bl...

We investigate selfadjoint positivity preserving C0-semigroups that are dominated by the free heat semigroup on Rd. Major examples are semigroups generated by Dirichlet Laplacians on open subsets or by Schrödinger operators with absorption potentials. We show explicit global Gaussian upper bounds for the kernel that correctly reflect the exponential decay of the semigroup. For eigenfunctions of...

0 Ts|Bt| dt t ) 1 2 ||L∞(Ω). for any family (At)t≥0 ∈ L(Ω, μ), (Bt)t≥0 ∈ L∞(Ω, μ) provided (Tt)t≥0 does not increase or decrease “too fast”. As an application, we prove a duality inequality for H − BMO spaces associated with general subordinated Poisson semigroups. All the results are proved in a more general setting, that is for (Bt)t≥0 and (At)t≥0 being families of elements of a semifinte von...