Abstract
We will give a complete description of \({\mathcal {I}}\) the set of all invertible quasicontinuous functions on the unit circle. In particular we will show that \({\mathcal {I}}\) has uncountably many path-connected components. We will also characterize \({\mathcal {F}}\) the set of Fredholm operators of the C\(^*\)-algebra generated by the Toeplitz operators \(T_\phi \) with quasicontinuous symbols \(\phi \). Finally we will classify the path-connected components of \({\mathcal {F}}\) and show that \({\mathcal {F}}\) has uncountably many path-connected components.
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Acknowledgements
The author would like to thank his PhD advisor Dr. Jingbo Xia, and dissertation committee members Dr. Lewis Coburn and Dr. Ching Chou for their help in completing this work. The author would also like to thank the reviewers for their helpful comments and suggestions on this paper.
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Communicated by Daniel Aron Alpay.
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Orenstein, A. Fredholm Operators in the Toeplitz Algebra \({\mathcal {I}}(QC)\) . Complex Anal. Oper. Theory 12, 1481–1496 (2018). https://doi.org/10.1007/s11785-017-0653-9
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DOI: https://doi.org/10.1007/s11785-017-0653-9