Commutator of composition operators with adjoints of composition operators

John H. Clifford, David Levi, Sivaram K. Narayan

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We characterize the compactness of the linear fractionally induced commutator in terms of the function theoretic properties of φ{symbol} and ψ. We show that in the automorphic case the commutator is compact if and only if φ{symbol} and ψ are simple rotations of the unit disc. On the other hand, when one of the inducing maps is not an automorphism of the disc, we show that the commutator is non-trivially compact if and only if the inducing maps are both parabolic with the same boundary fixed point or they are both hyperbolic with the same boundary fixed point and their other fixed points are conjugate reciprocals.

Original languageEnglish
Pages (from-to)677-686
Number of pages10
JournalComplex Variables and Elliptic Equations
Volume57
Issue number6
DOIs
StatePublished - Jun 2012

Keywords

  • commutator
  • compact operator
  • composition operator

Fingerprint

Dive into the research topics of 'Commutator of composition operators with adjoints of composition operators'. Together they form a unique fingerprint.

Cite this