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Toeplitz Quantization without Measure or Inner Product

  • Stephen Bruce SontzEmail author
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

This note is a follow-up to a recent paper by the author. Most of that theory is now realized in a new setting where the vector space of symbols is not necessarily an algebra nor is it equipped with an inner product, although it does have a conjugation. As in the previous paper one does not need to put a measure on this vector space. A Toeplitz quantization is defined and shown to have most of the properties as in the previous paper, including creation and annihilation operators. As in the previous paper this theory is implemented by densely defined Toeplitz operators which act in a Hilbert space, where there is an inner product, of course. Planck’s constant also plays a role in the canonical commutation relations of this theory. Proofs are given in order to provide a self-contained paper.

Keywords

Toeplitz operators Toeplitz quantization annihilation and creation operators 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Centro de Investigación en Matemáticas, A.C. (CIMAT)GuanajuatoMexico

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