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 , 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.
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Miroslav Engliš, Kévin Falk, Bruno Iochum, Spectral triples and Toeplitz operators. J. Noncommut. Geom. 9 (2015), no. 4, pp. 1041–1076DOI 10.4171/JNCG/215