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Closed range composition operators on BMOA. (English) Zbl 07355813

Summary: We employ a new reverse Carleson type condition and define a new sampling condition to study closed range composition operators on BMOA. We provide necessary and also sufficient conditions for a composition operator to be closed range on BMOA. We show that a composition operator is closed range as an operator from the Bloch space to BMOA if and only if it is bounded below on all Möbius transformations.

MSC:

47B33 Linear composition operators
47B38 Linear operators on function spaces (general)
30H10 Hardy spaces
30H20 Bergman spaces and Fock spaces
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
47B32 Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)
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References:

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