Abstract
So far our pursuit of compactness has dwelt on geometric issues associated with univalent inducing maps (cf. Chapters 3, 4, and 9). In this chapter we abandon univalence, and attack the compactness problem for composition operators induced by arbitrary holomorphic self-maps of the disc. As you might guess, the solution involves not only the geometry of the inducing map’s image, but its “affinity” for each of the points in this image.
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© 1993 Springer Science+Business Media New York
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Shapiro, J.H. (1993). Compactness: General Case. In: Composition Operators. Universitext: Tracts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0887-7_11
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DOI: https://doi.org/10.1007/978-1-4612-0887-7_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94067-0
Online ISBN: 978-1-4612-0887-7
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