In this survey article we describe how the recent work in quantization in multi-variable complex geometry (domains of holomorphy, symmetric domains, tube domains, etc.) leads to interesting results and problems in C*-algebras which can be viewed as examples of the "non-commutative geometry" in the sense of A. Connes. At the same time, one obtains new functional calculi (of pseudodifferential type) with possible applications to partial differential equations and group representations.
@article{bwmeta1.element.bwnjournal-article-bcpv38i1p385bwm,
author = {Upmeier, Harald},
title = {Toeplitz-Berezin quantization and non-commutative differential geometry},
journal = {Banach Center Publications},
volume = {38},
year = {1997},
pages = {385-400},
zbl = {0890.47017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv38i1p385bwm}
}
Upmeier, Harald. Toeplitz-Berezin quantization and non-commutative differential geometry. Banach Center Publications, Tome 38 (1997) pp. 385-400. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv38i1p385bwm/
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