Hankel operators and the Dixmier trace on the Hardy space
Review article, 2016

We give criteria for the membership of Hankel operators on the Hardy space on the disc in the Dixmier class, and establish estimates for their Dixmier trace. In contrast to the situation in the Bergman space setting, it turns out that there exist Dixmier-class Hankel operators that are not measurable (that is, their Dixmier trace depends on the choice of the underlying Banach limit), as well as Dixmier-class Hankel operators that do not belong to the Schatten-Lorentz ideal. A related question concerning logarithmic interpolation of Besov spaces is also discussed.


M. Englis

Slezska univerzita v Opave

Czech Academy of Sciences

Genkai Zhang

Chalmers, Mathematical Sciences, Analysis and Probability Theory

University of Gothenburg

Journal of the London Mathematical Society

0024-6107 (ISSN) 1469-7750 (eISSN)

Vol. 94 2 337-356

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