Entropy Numbers of Weighted Shifts

The main object of this paper is to establish a lower bound of the entropy numbers for powers of weighted shift operators on lp spaces, 1 ≤ p ≤ ∞, and we obtain some results of Pietsch. Furthermore, we get an interesting inequality between entropy numbers and s numbers of these shifts and, as a simple application of this inequality, we have, for q ∈ (0, ∞), that the two operator ideals E(e)q(lp, lp) and S(s)q(lp, lp) are identical.