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 Cφ is compact on BMOA, then Cφ is weakly compact on the X-valued space BMOAC(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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