  We address the problem of existence and uniqueness of solutions
$(c,u(\cdot))$ to ergodic Hamilton-Jacobi-Bellman (HJB) equations of the form
$H(x,\nabla u(x), D^{2}u(x)) = c$ in the whole space $\mathbb{R}^{m}$ with
unbounded and merely measurable data and where $H$ is a Bellman Hamiltonian.
The method we use is different from classical approaches. It relies on duality
theory and optimization in abstract Banach spaces together with maximal
dissipativity of the diffusion operator.
