Journal of Noncommutative Geometry


Full-Text PDF (386 KB) | Metadata | Table of Contents | JNCG summary
Volume 9, Issue 4, 2015, pp. 1041–1076
DOI: 10.4171/JNCG/215

Spectral triples and Toeplitz operators

Miroslav Engliš[1], Kévin Falk[2] and Bruno Iochum[3]

(1) Silesian University in Opava, Czech Republic
(2) CNRS Luminy, Marseille, France
(3) Aix-Marseille Université, France

We give examples of spectral triples, in the sense of A. Connes, constructed using the algebra of Toeplitz operators on smoothly bounded strictly pseudoconvex domains in $\mathbb C^n$, or the star product for the Berezin–Toeplitz quantization. Our main tool is the theory of generalized Toeplitz operators on the boundary of such domains, due to Boutet de Monvel and Guillemin.

Keywords: Toeplitz operator, pseudoconvex domain, spectral triple, Dixmier trace, Berezin–Toeplitz quantization

Engliš Miroslav, Falk Kévin, Iochum Bruno: Spectral triples and Toeplitz operators. J. Noncommut. Geom. 9 (2015), 1041-1076. doi: 10.4171/JNCG/215