Which linear-fractional
composition operators are essentially normal?
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Paul S. Bourdon, David Levi,
Sivaram K. Narayan, and Joel H. Shapiro
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Journal of Mathematical
Analysis and Applications 280 (2003) 30--53
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| Abstract: Building on earlier work of Howard Schwartz and Nina
Zorboska, we characterize the essentially normal composition
operators induced on the Hardy space H^2 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 H^2 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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