Abstract
In this note we study the maximal ideal space and invertibility problems in a Sarason-type algebra \(\mathcal{A}\) on the unit ball. By definition \(\mathcal{A}\) consists of all bounded measurable functions on the unit sphere for which the associated Hankel operator on the Hardy space is compact. We determine a natural closed subset of the maximal ideal space of \(\mathcal{A}\) and apply our results to show that the essential Taylor spectrum of all Toeplitz tuples with symbols in \(\mathcal{A}\) is connected.
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Eschmeier, J. (2014). On the Maximal Ideal Space of a Sarason-Type Algebra on the Unit Ball. In: Douglas, R., Krantz, S., Sawyer, E., Treil, S., Wick, B. (eds) The Corona Problem. Fields Institute Communications, vol 72. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1255-1_4
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DOI: https://doi.org/10.1007/978-1-4939-1255-1_4
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