, Volume 8, Issue 1, pp 111-127

Parabolic Non-Automorphism Induced Toeplitz-Composition C*-Algebras with Piece-wise Quasi-Continuous symbols

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In this paper we consider the C*-algebra $C^{*}(\{C_{\varphi }\}\cup \mathcal T (PQC(\mathbb T )))/K(H^{2})$ generated by Toeplitz operators with piece-wise quasi-continuous symbols and a composition operator induced by a parabolic linear fractional non-automorphism symbol modulo compact operators on the Hilbert-Hardy space $H^{2}$ . This C*-algebra is commutative. We characterize its maximal ideal space. We apply our results to the question of determining the essential spectra of linear combinations of a class of composition operators and Toeplitz operators.

Communicated by Gadadhar Misra.
Dedicated to Prof. Thomas L. Kriete for his 70th birthday.