μ-Hankel operators on Hilbert spaces

Abstract

A class of operators is introduced ($\mu$-Hankel operators, $\mu$ is a complex parameter), which generalizes the class of Hankel operators. Criteria for boundedness, compactness, nuclearity, and finite dimensionality are obtained for operators of this class, and for the case $\mu=1$ their description in the Hardy space is given. Integral representations of $\mu$-Hankel operators on the unit disk and on the Semi-Axis are also considered.