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Composition operators within singly generated composition C*-algebras

Thomas Kriete·Barbara MacCluer·Jennifer Moorhouse
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Abstract

Let $ϕ$ be a linear-fractional self map of the open unit disk, not an automorphism, such that $ϕ(ζ)=η$ for distinct points $ζ,η$ in the unit circle. We consider the question of which composition operators lie in the unital C*-algebra generated by the composition operator $C_ϕ$ and the ideal of compact operators, acting on the Hardy space $H^2$.

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Thomas Kriete, Barbara MacCluer, Jennifer Moorhouse. 2008-10-31. Composition operators within singly generated composition C*-algebras. https://arxiv.org/abs/math/0610077

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