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Adjoints of linear fractional composition operators on weighted Hardy spaces

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Abstract

It is well known that on the Hardy space H2({ie651-1}) or weighted Bergman space A 2α ({ie651-1}) over the unit disk, the adjoint of a linear fractional composition operator equals the product of a composition operator and two Toeplitz operators. On S2({ie651-1}), the space of analytic functions on the disk whose first derivatives belong to H2({ie651-1}), Heller showed that a similar formula holds modulo the ideal of compact operators. In this paper we investigate what the situation is like on other weighted Hardy spaces.

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Acknowledgements

The authors wish to thank the referee for a careful reading and useful comments that improved the presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Toledo, Mail Stop 942, Toledo, OH, 43606, USA

    Željko Čučković & Trieu Le

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  1. Željko Čučković
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  2. Trieu Le
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Correspondence to Željko Čučković.

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Communicated by L. Kérchy

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Čučković, Ž., Le, T. Adjoints of linear fractional composition operators on weighted Hardy spaces. ActaSci.Math. 82, 651–662 (2016). https://doi.org/10.14232/actasm-015-801-z

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  • DOI: https://doi.org/10.14232/actasm-015-801-z

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