Entropy Numbers of General Diagonal Operators

We determine the asymptotic behavior of the entropy numbers of diagonal operators D : `p ! `q, (xk) 7! (_kxk), 0 < p, q _ 1, under mild regularity and decay conditions on the generating sequence (_k). Our results extend the known estimates for polynomial and logarithmic diagonals (_k). Moreover, we also consider some exotic intermediate examples like _k = exp(&#8722;plog k)