T. Kuhn

Entropy Numbers of Diagonal Operators of Logarithmic Type

We determine the asymptotic behaviour (as $k\rightarrow \infty$, up to multiplicative constants not depending on k) of the entropy numbers $e_{k}$ $(D_{\sigma} : \linebreak l_p\rightarrow l_q)$, $ 1\leq p \leq q\leq \infty,$ of diagonal operators generated by logarithmically decreasing sequences $\sigma = (\sigma_n)$. This complements earlier results by Carl (1981) who investigated the case of power-like decay of the diagonal.