# Absolutely continuous spectrum for periodic Jacobi operators

I've been reading Gerald Teschl's book on Jacobi operators (and nonlinear lattices) where chapter seven shows how to compute the spectrum of a bi-infinite periodic Jacobi operator. I was wondering what can be said for the half line example, i.e. a one-way infinite periodic Jacobi operator. For instance, is the spectrum still purely absolutely continuous?

• No, you can have eigenvalues in the gaps, and of course the multiplicity of the ac spectrum will be $1$ now. Nothing else changes. – Christian Remling Feb 1 at 20:32
• Thanks very much! – Mathmo Feb 1 at 21:45