Generalized Foguel-Hankel Operators

Nikolaos Chalmoukis; Giovanni Marano

functional analysis

Generalized Foguel-Hankel Operators

arXiv:2601.19599

summary

The paper defines a broader class of Foguel‑Hankel operators by replacing the unilateral shift with a general multiplication operator on the Hardy space, studies when these operators are power bounded via Peller’s condition, and shows that for the Hilbert matrix case similarity to a contraction coincides with the Kreiss condition.

Abstract

In this paper we introduce a more general class of Foguel-Hankel operators, where the unilateral shift on $ℓ^{2} (N)$ is replaced by a general multiplication operator on the Hardy space $H^{2}$ . We prove that Peller's condition is sufficient for the operator to be power bounded, but in general it is not necessary. When the Hankel matrix is the Hilbert matrix, we prove that being similar to a contraction is equivalent to the (a priori) weaker Kreiss condition.

Minor corrections

Topics & keywords

#foguel-hankel operators #hardy space #power boundedness #kreiss condition #hilbert matrix #operator similarityFoguel-Hankel operatormultiplication operatorPeller's conditionpower boundedKreiss conditioncontraction similarityHilbert matrix