**Abstract: **
This is an application of the KAM iterative procedure but for hamiltonians
of the form H_0+V with H_0>0 and block diagonal and V symmetric
and only H_0 form bounded. Under some spacing conditions between the
spectrum of the blocks and a condition on the "size" of V we construct
at once the unitary transform which block diagonalizes H_0+V.
This is then used to study the spectral nature of Floquet
Hamiltonians with unbounded time dependent perturbations. Other
applications are possible.

See

P. Duclos, O. Lev, P. Stovicek, M. Vittot: Weakly
regular Floquet Hamiltonians with pure point spectrum, preprint
CPT2001/.P4189; submitted to Commun. Math. Phys.,
mp_arc 01-115

and

P. Duclos, O. Lev, P. Stovicek, M. Vittot: Progressive
diagonalization and applications, to appear in the Proceedings of the
conference "Operator Algebras and Mathematical Physics", Constanta, July
2001