Which linear-fractional composition operators
are essentially normal?

 

Paul S. Bourdon, David Levi,

Sivaram K. Narayan, and Joel H. Shapiro

 

Journal of Mathematical Analysis and Applications 280 (2003) 30--53
 
Abstract: Building on earlier work of Howard Schwartz and Nina Zorboska, 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 non-automorphisms. These parabolic maps induce the first known examples of nontrivially essentially normal composition operators. In addition we characterize those linear-fractional 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.

 

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