Fuglede-Kadison determinants of matrix-valued semicircular elements and capacity estimates

We calculate the Fuglede-Kadison determinant of arbitrary matrix-valued semicircular operators in terms of the capacity of the corresponding covariance mapping. We also improve a lower bound by Garg, Gurvits, Oliveira, and Widgerson on this capacity, by making it dimension-independent.

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Bibliographische Detailangaben
Hauptverfasser:	Mai, Tobias, Speicher, Roland
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics - Functional Analysis Mathematics - Operator Algebras Mathematics - Rings and Algebras
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Beschreibung
Zusammenfassung:	We calculate the Fuglede-Kadison determinant of arbitrary matrix-valued semicircular operators in terms of the capacity of the corresponding covariance mapping. We also improve a lower bound by Garg, Gurvits, Oliveira, and Widgerson on this capacity, by making it dimension-independent.
DOI:	10.48550/arxiv.2406.15922