Composition Operators within Singly Generated Composition C * -algebras
نویسنده
چکیده
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 question of which composition operators lie in C∗(Cφ,K), the unital C∗-algebra generated by the composition operator Cφ and the ideal K of compact operators, acting on the Hardy space H. 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.
منابع مشابه
ar X iv : m at h / 06 10 07 7 v 1 [ m at h . FA ] 2 O ct 2 00 6 COMPOSITION OPERATORS WITHIN SINGLY GENERATED COMPOSITION C ∗ - ALGEBRAS
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 question of which composition operators lie in C∗(Cφ,K), the unital C∗-algebra generated by the composition operator Cφ and the ideal K of compact operators, acting on the Hardy space H.
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