Criteria for the absolutely continuous spectral components of matrix-valued Jacobi operators

We extend in this work the Jitomirskaya-Last inequality [Power-law subordinacy and singular spectra i. Half-line operators, Acta Math. 183 (1999) 171-189] and Last and Simon [Eigenfunctions, transfer matrices, and absolutely continuous spectrum of onedimensional Schrodinger operators, Invent. Math. 135 (1999) 329-367] criterion for the absolutely continuous spectral component of a half-line Schrodinger operator to the special class of matrix-valued Jacobi operators H : l(2)(Z, C-l) -> l(2)(Z, C-l) given by the law [Hu](n) := D(n-1)u(n-1) + D(n)u(n+1) +V(n)u(n), where (D-n)(n) (V-n)(n) are bilateral sequences of l x l self-adjoint matrices such that 0 < inf(n is an element of z) s(l) [D-n] <= sup(n is an element of z) s(1)[D-n] < infinity (here, s(k)[A] stands for the kth singular value of A). Moreover, we also show that the absolutely continuous components of even multiplicity of minimal dynamically defined matrix-valued Jacobi operators are constant, extending another result from Last and Simon [Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrodinger operators, Invent. Math. 135 (1999) 329-367] originally proven for scalar Schrodinger operators.