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Closed Range Composition Operators on BMOA

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Abstract

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.

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Acknowledgements

We thank the referee for his/her comments that improved the quality of the paper.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, 45221, USA

    Kevser Erdem

  2. Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR, 72701, USA

    Maria Tjani

Authors
  1. Kevser Erdem
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  2. Maria Tjani
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Correspondence to Maria Tjani.

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Communicated by Isabelle Chalendar.

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Erdem, K., Tjani, M. Closed Range Composition Operators on BMOA. Complex Anal. Oper. Theory 15, 51 (2021). https://doi.org/10.1007/s11785-021-01104-8

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  • DOI: https://doi.org/10.1007/s11785-021-01104-8

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