Exponential dichotomy for dynamically defined matrix-valued Jacobi operators

The paper proves, for dynamically defined matrix-valued Jacobi operators with minimal base and invertible D, that for each ω one has ρ(H_ω) = {z : (T,A_z) ∈ UG} = {z : (T,A_z) ∈ UH}. Its route is: (i) establish UG ⇔ UH for SL(2l,C)-cocycles (Theorem 1.3), then (ii) prove the inclusions ρ(H_ω) ⊆ {z : UG} and the converse via spectral-measure methods and an explicit Green’s function construction, yielding Corollary 1.6 (and independence of ω) . The candidate model solution proves the same characterization but organizes the argument differently: (1) a Johnson-type resolvent ⇔ UH step via Green kernels; (2) UH ⇒ UG by a blocking/transversality estimate; (3) UG ⇒ UH via general dichotomy theory (expansivity ⇔ exponential dichotomy). The paper’s proofs are correct and complete for its assumptions, and the model’s proof outline is also correct, though it relies on standard (but externally cited) dichotomy theory rather than the paper’s specific spectral-measure route. Hence, both are correct, with different proofs.