  In this paper, we revisit the Riemann--Liouville analytic semigroup. In
particular, we completely characterize the membership to the Schatten class
$S^r$ on $L^2(0,1)$, as well as the membership to the class of nuclear
operators on $L^p(0,1)$, $p\geq 1$, and the membership to the ideal of
absolutely $r$-summing operators for any $r\geq 1$.
