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Composition operators within singly generated composition C*-algebras

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Abstract

Let ϕ be a linear-fractional self-map of the open unit disk D, not an automorphism, such that ϕ(ζ) = η for two distinct points ζ,η in the unit circle ∂D. We consider the problem of determining which composition operators, acting on the Hardy space H 2, lie in C*(C ϕ ,K), the unital C*-algebra generated by the composition operator C ϕ and the ideal K of compact operators. This necessitates a companion study of the unital C*-algebra generated by the composition operators induced by all parabolic non-automorphisms with common fixed point on the unit circle.

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Authors and Affiliations

  1. Department of Mathematics, University of Virginia, PO Box 400137, Charlottesville, VA, 22904, USA

    Thomas L. Kriete & Barbara D. MacCluer

  2. Department of Mathematics, Colgate University, Hamilton, NY, 13356, USA

    Jennifer L. Moorhouse

Authors
  1. Thomas L. Kriete
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  2. Barbara D. MacCluer
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  3. Jennifer L. Moorhouse
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Correspondence to Thomas L. Kriete.

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Kriete, T.L., MacCluer, B.D. & Moorhouse, J.L. Composition operators within singly generated composition C*-algebras. Isr. J. Math. 179, 449–477 (2010). https://doi.org/10.1007/s11856-010-0089-7

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  • DOI: https://doi.org/10.1007/s11856-010-0089-7

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