A note on the nonuniform exponential stability and dichotomy for nonautonomous difference equations

In their recent result Hu and Mitsui proved that any exponentially stable nonautonomous linear difference equation can be reduced via suitable change of variables to equivalent linear difference equations whose coefficient matrices have spectral norm which is less then 1. In the present paper, we prove that this statement holds under weaker assumption that the nonautonomous linear difference equation is (strongly) nonuniformly exponentially stable. Moreover, we also establish corresponding results in the case of strong nonuniform exponential dichotomies.