What Do Composition Operators Know About Inner Functions?
- Cite this article as:
- Shapiro, J. Mh Math (2000) 130: 57. doi:10.1007/s006050050087
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This paper gives several different ways in which operator norms characterize those composition operators \(\) that arise from holomorphic self-maps ϕ of the unit disc that are inner functions. The setting is the Hardy space H2 of the disc, and the key result is a characterization of inner functions in terms of the asymptotic behavior of the Nevanlinna counting function. The case \(\) offers an interesting surprise.