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 ℂn 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 SB generated by a finite Blaschke product B. We then use the description of the numerical range of SB as intersection of Poncelet polygons, a special representation of Blaschke products related to boundary interpolation, and an explicit formula for the barycenter of the vertices of Poncelet polygons involving elliptic functions.
- Standort
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Deutsche Nationalbibliothek Frankfurt am Main
- Umfang
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Online-Ressource
- Sprache
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Englisch
- Erschienen in
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On partial isometries with circular numerical range ; volume:8 ; number:1 ; year:2021 ; pages:176-186 ; extent:11
Concrete operators ; 8, Heft 1 (2021), 176-186 (gesamt 11)
- Urheber
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Wegert, Elias
Spitkovsky, Ilya
- DOI
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10.1515/conop-2020-0121
- URN
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urn:nbn:de:101:1-2410301539006.314421098725
- Rechteinformation
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Letzte Aktualisierung
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15.08.2025, 07:23 MESZ
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Beteiligte
- Wegert, Elias
- Spitkovsky, Ilya
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