  We extend in this work the Jitomirskaya-Last inequality and
Last-Simoncriterion for the absolutely continuous spectral component of a
half-line Schr\"odinger operator to the special class of matrix-valued Jacobi
operators $H:l^2(\mathbb{Z},\mathbb{C})\rightarrow l^2(\mathbb{Z},\mathbb{C})$
given by the law $[H \textbf{u}]_{n} := D_{n - 1} \textbf{u}_{n - 1} + D_{n}
\textbf{u}_{n + 1} + V_{n} \textbf{u}_{n}$, where $(D_n)_n$ and $(V_n)_n$ are
bilateral sequences of $l\times l$ self-adjoint matrices such that
$0<\inf_{n\in\mathbb{Z}}s_l[D_n]\le\sup_{n\in\mathbb{Z}}s_1[D_n]<\infty$ (here,
$s_k[A]$ stands for the $k$-th 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-Simon originally proven for scalar
Schr\"odinger operators.
