Abstract
A function theoretic characterization is given of when a composition operator is compact on BMOA, the space of analytic functions on the unit disk having radial limits that are of bounded mean oscillation on the unit circle. When the symbol of the composition operator is univalent, compactness on BMOA is shown to be equivalent to compactness on the Bloch space, and a characterization in terms of the geometry of the image of the disk under the symbol of the operator results.
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