Abstract
In this paper, we show that on the weighted Bergman space of the unit disk the essential norm of a noncompact Hankel operator equals its distance to the set of compact Hankel operators and is realized by infinitely many compact Hankel operators, which is analogous to the theorem of Axler, Berg, Jewell and Shields on the Hardy space in Axler et al. (Ann Math 109:601–612, 1979); moreover, the distance is realized by infinitely many compact Hankel operators with symbols continuous on the closure of the unit disk and vanishing on the unit circle.
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F. Li was supported by China Scholarship Council.
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Li, F. Essential Norm of Toeplitz Operators and Hankel Operators on the Weighted Bergman Space. Integr. Equ. Oper. Theory 75, 517–525 (2013). https://doi.org/10.1007/s00020-012-2024-2
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DOI: https://doi.org/10.1007/s00020-012-2024-2