Two Lower Estimates in Greedy Approximation

We prove one lower estimate for the rate of convergence of the Pure Greedy Algorithm with regard to a general dictionary and another lower estimate for the rate of convergence of the Weak Greedy Algorithm with a special weakness sequence τ = {t}, 0 < t < 1, with regard to a general dictionary. The second lower estimate combined with the known upper estimate gives the right (in the sense of order) dependence of the exponent in the rate of convergence on the parameter t when t ↠ 0.