Composition operators within singly generated composition C*-algebras

Abstract

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

21 pages; minor revision of earlier version

References in corpus (2)

• Toeplitz-Composition C*-Algebras
• C*-algebras generated by groups of composition operators