Spectral triples and Toeplitz operators (Q5963563)

\textit{L. Boutet de Monvel} and \textit{V. Guillemin} [The spectral theory of Toeplitz operators. Princeton University Press; University of Tokyo Press (1981; Zbl 0469.47021)] developed a theory of Toeplitz operators with pseudo-differential symbols. The authors of the paper under review construct several spectral triples based on generalized Toeplitz operators on Hardy and Bergman spaces over smoothly bounded strictly pseudo-convex domains \(\Omega\) in \(\mathbb{C}\). Such spectral triples encode the Cauchy-Riemann geometry of \(\Omega\) and the corresponding Riemannian manifolds. The paper interrelates many interesting and important topics.