Which linear-fractional composition operators are essentially normal?

Paul S. Bourdon, David Levi, Sivaram K. Narayan, Joel H. Shapiro

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


We characterize the essentially normal composition operators induced on the Hardy space H2 by linear-fractional maps; they are either compact, normal, or (the nontrivial case) induced by parabolic nonautomorphisms. These parabolic maps induce the first known examples of nontrivially essentially normal composition operators. In addition, we characterize those linear-fractionally induced composition operators on H2 that are essentially self-adjoint, and present a number of results for composition operators induced by maps that are not linear-fractional.

Original languageEnglish
Pages (from-to)30-53
Number of pages24
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - Apr 1 2003


  • Composition operator
  • Essentially normal
  • Linear-fractional map


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