Strict singularity of a Volterra-type integral operator on $H^p$

Abstract

acting on the Hardy spaces Hp of the unit disc. The operator Tg was introduced by Ch. Pommerenke and it has been studied systematically by several people including A. Aleman, A.G. Siskakis and R. Zhao among others. From a functional analytic point of view, one interesting notion is the strict singularity of a linear operator between Banach spaces. An operator is strictly singular if its restriction to any infinite-dimensional subspace is not an isomorphism onto its range. We discuss our recent result, which states that a non-compact Tg fixes an isomorphic copy of the sequence space lp. In particular, the strict singularity of Tg coincides with its compactness on spaces Hp.