2021
DOI: 10.48550/arxiv.2109.08481
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On partial isometries with circular numerical range

Abstract: In their LAMA'2016 paper Gau, Wang and Wu conjectured that a partial isometry A acting on C n cannot have a circular numerical range with a non-zero center, and proved this conjecture for n ≤ 4. We prove it for operators with rank A = n − 1 and any n.The proof is based on the unitary similarity of A to a compressed shift operator S B generated by a finite Blaschke product B. We then use the description of the numerical range of S B as intersection of Poncelet polygons, a special representation of Blaschke prod… Show more

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