Eventual Ideal Properties of the Riemann-Liouville Analytic Semigroup

Abstract

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 $L^p(0,1)$, $p\ge 1$, and the membership to the ideal of absolutely $r$-summing operators for any $r\ge 1$.