Estimates of Green matrix entries of selfadjoint unbounded block Jacobi matrices

In a wide class of block Jacobi matrices, an estimate of norms of Green matrix (resolvent) entries is proved, which depends on the rate of growth of norms of the off-diagonal entries of the matrix and on the distance from the spectral parameter to the essential spectrum if the latter is nonempty. The sharpness of this estimate is shown by an example.