Entropy Numbers of Vector-Valued Diagonal Operators Original Research Article

Let Iα: lq(l2jp)→lq(l2j∞) be a diagonal operator assigning to vector-coordinate xj∈l2jp the vector-value j−αxj. We prove the estimates of entropy numbers of Iα. The results confirm the conjecture stated in a recent paper by Cobos and Kühn, and extend their results to quasi-Banach setting.