Eventual Ideal Properties of the Riemann-Liouville Analytic Semigroup

TL;DR

This paper thoroughly characterizes the properties of the Riemann-Liouville analytic semigroup, focusing on its membership in various operator classes on different function spaces, advancing understanding of its ideal properties.

Contribution

It provides a complete characterization of the semigroup's membership in Schatten, nuclear, and absolutely r-summing classes on relevant function spaces.

Findings

Characterization of Schatten class membership on L^2(0,1)

Identification of nuclear operator membership on L^p(0,1) for p ≥ 1

Determination of absolutely r-summing operator membership for r ≥ 1

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