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Toeplitz-composition algebras generated by piecewise quasicontinuous symbols and a linear fractional non-automorphism fixing a boundary point

机译:Toeplitz-composition algebras generated by piecewise quasicontinuous symbols and a linear fractional non-automorphism fixing a boundary point

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摘要

Commutative Toeplitz-composition subalgebras of the Calkin algebra on the classical Hardy space are analyzed with piecewise quasicontinuous symbols and a linear fractional non-automorphism fixing a boundary point. For the parabolic case the fiber structure of the maximal ideal space of the C*-subalgebra is explicitly described, resulting in essential spectrum and essential norm formulas. For the non-parabolic case, the Shilov boundary of a non-self-adjoint subalgebra is identified and essential spectra obtained. The subalgebra, although not maximal commutative, preserves spectra in the Calkin algebra. Fredholm index formulas are obtained for both cases. (c) 2022 Elsevier Inc. All rights reserved.

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