Compact Hankel Operators Between Distinct Hardy Spaces and Commutators

Karol Leśnik; Paweł Mleczko

doi:10.1007/s00020-021-02668-y

Compact Hankel Operators Between Distinct Hardy Spaces and Commutators

Integral Equations and Operator Theory ◽

10.1007/s00020-021-02668-y ◽

2021 ◽

Vol 93 (5) ◽

Author(s):

Karol Leśnik ◽

Paweł Mleczko

Keyword(s):

Hardy Spaces ◽

Toeplitz Operators ◽

Essential Norm ◽

Hankel Operators

AbstractThe paper is devoted to the study of compactness of Hankel operators acting between distinct Hardy spaces generated by Banach function lattices. We prove an analogue of Hartman’s theorem characterizing compact Hankel operators in terms of properties of their symbols. As a byproduct we give an estimation of the essential norm of such operators. Furthermore, compactness of commutators and semicommutators of Toeplitz operators for unbounded symbols is discussed.

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Hankel operators with PC symbols and the space H∞ + PC

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500032327 ◽

1981 ◽

Vol 89 (1-2) ◽

pp. 17-24 ◽

Cited By ~ 1

Author(s):

F. F. Bonsall ◽

T. A. Gillespie

Keyword(s):

Unit Circle ◽

Explicit Formula ◽

Hardy Spaces ◽

Hankel Operator ◽

Essential Norm ◽

Hankel Operators ◽

Continuous Functions ◽

Piecewise Continuous ◽

The Way

SynopsisWe obtain an explicit formula for the essential norm of a Hankel operator with its symbol in the space PC, which is the closure in L∞ of the space of piecewise continuous functions on the unit circle . It follows from this formula that functions in PC can be approximated as closely by functions in C, the continuous functions on the circle, as by functions in the much larger space H∞ + C. This is an example of the way in which properties of the Hardy spaces can be derived from properties of Hankel operators.

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Essential Norm of Toeplitz Operators and Hankel Operators on the Weighted Bergman Space

Integral Equations and Operator Theory ◽

10.1007/s00020-012-2024-2 ◽

2012 ◽

Vol 75 (4) ◽

pp. 517-525 ◽

Cited By ~ 2

Author(s):

Fengying Li

Keyword(s):

Bergman Space ◽

Toeplitz Operators ◽

Essential Norm ◽

Hankel Operators ◽

Weighted Bergman Space

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The Berezin Transform of Toeplitz Operators on the Weighted Bergman Space

Potential Analysis ◽

10.1007/s11118-021-09915-2 ◽

2021 ◽

Author(s):

Cezhong Tong ◽

Junfeng Li ◽

Hicham Arroussi

Keyword(s):

Bergman Space ◽

Toeplitz Operators ◽

Reproducing Kernel ◽

Bergman Spaces ◽

Essential Norm ◽

Berezin Transform ◽

Weighted Bergman Space ◽

Weighted Bergman Spaces ◽

Kernel Estimates ◽

Berezin Transforms

AbstractIn this paper, we obtain some interesting reproducing kernel estimates and some Carleson properties that play an important role. We characterize the bounded and compact Toeplitz operators on the weighted Bergman spaces with Békollé-Bonami weights in terms of Berezin transforms. Moreover, we estimate the essential norm of them assuming that they are bounded.

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