In this note we consider the homogenization problem for a matrix locally periodic elliptic operator on Rd of the form Aε = −divA(x, x/ε)∇. The function A is assumed to be Hölder continuous with exponent s ∈ [0, 1] in the “slow” variable and bounded in the “fast” variable. We construct approximations for (Aε − μ)−1, including one with a corrector, and for (−Δ)s/2(Aε − μ)−1 in the operator norm on L2(Rd)n. For s ≠ 0, we also give estimates of the rates of approximation.