Trace formulas and Borg-type theorems for matrix-valued Jacobi and Dirac finite difference operators

Borg-type uniqueness theorems for matrix-valued Jacobi operators H and supersymmetric Dirac difference operators D are proved. More precisely, assuming reflectionless matrix coefficients A,B in the self-adjoint Jacobi operator H=AS++A-S-+B (with S± the right/left shift operators on the lattice ) and the spectrum of H to be a compact interval [E-,E+], E-