Integral Equations and Operator Theory

, Volume 25, Issue 3, pp 329-335

First online:

Local spectral theory for invertible composition operators onH p

  • R. C. SmithAffiliated withDepartment of Mathematics and Statistics, Mississippi State University

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Invertible composition operators on the Hardy spaceH p have automorphic symbols. For 1<p<∞ andp≠2 it is shown that some elliptic composition operators are scalar while others are generalized scalar but not spectral, that parabolic composition operators are generalized scalar but not spectral and that hyperbolic composition operators do not have the single-valued extension property.

AMS Subject Classification

47B40 47B38