Schmidt subspaces of Hankel operators

TL;DR

This paper investigates the structure of Schmidt subspaces of bounded Hankel operators on Hardy spaces, extending previous studies to include the conjugate symbols and providing new insights into their spectral properties.

Contribution

It characterizes Schmidt subspaces of Hankel operators and explores the range of operators with conjugate symbols, advancing understanding of their spectral and functional structure.

Findings

Characterization of Schmidt subspaces for Hankel operators

Analysis of the range of Hankel operators with conjugate symbols

Extension of previous results to new classes of symbols

Abstract

We consider bounded Hankel operators $H_{\psi}$ acting on the Hardy space $H^2$ to $L^2\ominus H^2$ and obtain results on the Schmidt subspaces $E^+_s(H_\psi)$ of such operators defined as the kernels of $ H_{\psi}^{\ast}H_{\psi}-s^2I$ where $s>0$. These spaces have been recently studied in \cite{GP} and \cite{GP1} in the context of anti-linear Hankel operators. We also discuss the range of the Hankel operators with symbols being the complex conjugates of functions in the unit ball of $H^{\infty}$.