Spectral triples and Toeplitz operators

  • Miroslav Engliš

    Silesian University in Opava, Czech Republic
  • Kévin Falk

    CNRS Luminy, Marseille, France
  • Bruno Iochum

    Aix-Marseille Université, France

Abstract

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 Cn\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.

Cite this article

Miroslav Engliš, Kévin Falk, Bruno Iochum, Spectral triples and Toeplitz operators. J. Noncommut. Geom. 9 (2015), no. 4, pp. 1041–1076

DOI 10.4171/JNCG/215