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It is well known that one can often construct a star-product by expanding the product of two Toeplitz operators asymptotically into a series of other Toeplitz operators multiplied by increasing powers of the Planck constant h. This is the Berezin-Toeplitz quantization. We show that one can obtain in a similar way in fact any star-product which is equivalent to the Berezin-Toeplitz star-product, by using instead of Toeplitz operators other suitable mappings from compactly supported smooth functions to bounded linear operators on the corresponding Hilbert spaces. A crucial ingredient in the proof is the generalization, due to Colombeau, of the classical theorem of Borel on the existence of a function with prescribed derivatives of all orders at a point, which reduces the proof to a construction of a locally convex space enjoying some special properties.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
77-93
Opis fizyczny
Daty
wydano
2007
Twórcy
autor
- Mathematics Institute, Žitná 25, 11567 Praha 1, Czech Republic
- Mathematics Institute, Na Rybníčku 1, 74601 Opava, Czech Republic
autor
- Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FIN-00014 Helsinki, Finland
Bibliografia
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_4064-sm180-1-6