KAM theory for the Hamiltonian derivative wave equation

We prove an infinite dimensional KAM theorem which implies the existence of Cantor families of small-amplitude, reducible, elliptic, analytic, invariant tori of Hamiltonian derivative wave equations. A key concept is the introduction of the class of quasi-Toplitz Hamiltonians, which provides a sharp asympototic decay estimate for the eigenvalues of the linearized operators at each KAM step.