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Hankel operators and the Dixmier trace on the Hardy space
Author(s) -
Engliš Miroslav,
Zhang Genkai
Publication year - 2016
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdw037
Subject(s) - mathematics , trace (psycholinguistics) , lorentz space , hardy space , pure mathematics , trace class , nuclear operator , class (philosophy) , space (punctuation) , interpolation (computer graphics) , interpolation space , logarithm , banach space , ideal (ethics) , lorentz transformation , mathematical analysis , approximation property , hilbert space , functional analysis , image (mathematics) , computer science , philosophy , artificial intelligence , linguistics , chemistry , operating system , biochemistry , epistemology , classical mechanics , physics , gene
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 existDixmier‐ classHankel operators that are not measurable (that is, their Dixmier trace depends on the choice of the underlying Banach limit), as well asDixmier‐ classHankel operators that do not belong to the ( 1 , ∞ ) Schatten–Lorentz ideal. A related question concerning logarithmic interpolation of Besov spaces is also discussed.