Berezin–Toeplitz Operators

  • Yohann Le FlochEmail author
Part of the CRM Short Courses book series (CRMSC)


As before, let \((M, \omega )\) be a prequantizable, compact, connected Kähler manifold, let \(L \rightarrow M\) be a prequantum line bundle, and let \(\mathcal {H}_k\) be the associated Hilbert spaces. Let \(L^2(M, L^k)\) be the completion of the space of smooth sections of \(L^k \rightarrow M\) with respect to the inner product \(\langle \,\cdot \,,\cdot \, \rangle _k\) introduced earlier, and let \(\varPi _k\) be the orthogonal projector from \(L^2(M, L^k)\) to \(\mathcal {H}_k\). This projector is often called the Szegő projector.

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.IRMAUniversité de StrasbourgStrasbourgFrance

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