Abstract
AbstractIn 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.KeywordsSarason algebraMaximal ideal spaceToeplitz tuplesEssential spectrumSubject ClassificationsPrimary 47A13Secondary 47B3546J15
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