Schatten class Hankel operators on the Segal-Bargmann space and the Berger-Coburn phenomenon

TL;DR

This paper revisits and corrects key theorems related to Schatten class Hankel operators on the Segal-Bargmann space, clarifying their properties and the Berger-Coburn phenomenon.

Contribution

The authors provide a corrected proof of a main theorem and an accurate statement of a secondary theorem concerning Hankel operators in the Segal-Bargmann space.

Findings

Corrected proof of Theorem 1.2

Corrected statement of Theorem 2.6

Clarification of the Berger-Coburn phenomenon

Abstract

The authors provide a correct proof of Theorem 1.2 and correct the statement of Theorem 2.6 in their paper, which appeared in Trans. Amer. Math. Soc. 375 (2022), 3733-3753.