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.
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
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