Simplicity of singular spectrum in Anderson type Hamiltonians
نویسندگان
چکیده
We study self adjoint operators of the form Hω = H0 + ∑ ω(n)(δn| · )δn, where the δn’s are a family of orthonormal vectors and the ω(n)’s are independent random variables with absolutely continuous probability distributions. We prove a general structural theorem which provides in this setting a natural decomposition of the Hilbert space as a direct sum of mutually orthogonal closed subspaces that are almost surely invariant under Hω and which is helpful for the spectral analysis of such operators. We then use this decomposition to prove that the singular spectrum of Hω is almost surely simple.
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