Explores the circular numerical ranges of partial isometries, indicating unique properties of mathematical functions.
We introduce the reader to partial isometries and their properties. In particular, we consider the Gau-Wang-Wu conjecture from 2016: When is the numerical range of a partial isometry circular? In order to describe a simple proof of a special case of the conjecture, we discuss basic properties of Blaschke products, compressions of the shift operator and some classical geometric methods.
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Adams et al. (2026) studied this question.
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