In this paper we prove that the one dimensional Schrόdinger operator on 1 2 (Z) with potential given by:has a Cantor spectrum of zero Lebesgue measure for any irrational α and any λ>0. We can thus extend the Kotani result on the absence of absolutely continuous spectrum for this model, to all xeT.

We consider the C*-algebras which contain the Weyl operators when the symplectic form which defines the C.C.R. is possibly degenerate. We prove that the C.C.R. are all obtained as a quotient of a universal C*-algebra by some of its ideals, and we characterize all these ideals.