**T. Kuhn**

## Entropy Numbers of Diagonal Operators of Logarithmic Type

**abstract:**

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.