The almost reducibility conjecture for analytic almost periodic Jacobi cocycles

Let $(\beta,A_\epsilon^E)$ be an analytic almost periodic Jacobi cocycle, and suppose that its determinant is bounded away from zero. Almost reducibility conjecture for Jacobi cocycles. Sub-critical behavior of $(\beta,A_\epsilon^E)$ implies purely absolutely continuous spectrum. The claim is proposed as a version of the almost reducibility conjecture adapted to Jacobi cocycles after examples show that the unrestricted statement can fail when the off-diagonal function has zeros; the source gives no resolution under the bounded-determinant hypothesis.