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Composition Operators and Vector-valued BMOA

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Abstract.

Analytic composition operators \(C_{\varphi}: f \mapsto f \, o\, \varphi\) are studied on X-valued versions of BMOA, the space of analytic functions on the unit disk that have bounded mean oscillation on the unit circle, where X is a complex Banach space. It is shown that if X is reflexive and C φ is compact on BMOA, then C φ is weakly compact on the X-valued space BMOA C (X) defined in terms of Carleson measures. A related function-theoretic characterization is given of the compact composition operators on BMOA.

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  1. Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FIN-00014, Helsinki, Finland

    Jussi Laitila

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  1. Jussi Laitila
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Correspondence to Jussi Laitila.

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Laitila, J. Composition Operators and Vector-valued BMOA. Integr. equ. oper. theory 58, 487–502 (2007). https://doi.org/10.1007/s00020-007-1503-3

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  • DOI: https://doi.org/10.1007/s00020-007-1503-3

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