Toeplitz Quantization of a Free $ * $-Algebra
Abstract
In this note we quantize the free -algebra generated by finitely many variables, which is a new example of the theory of Toeplitz quantization of -algebras as developed previously by the author. This is achieved by defining Toeplitz operators with symbols in that non-commutative free -algebra. These are densely defined operators acting in a Hilbert space. Then creation and annihilation operators are introduced as special cases of Toeplitz operators, and their properties are studied.
Cite
@article{arxiv.1905.00913,
title = {Toeplitz Quantization of a Free $ * $-Algebra},
author = {Stephen Bruce Sontz},
journal= {arXiv preprint arXiv:1905.00913},
year = {2019}
}
Comments
10 pages. Portions of this work previously appeared in Section 8 of arXiv:1308.5454v2, but not in the final version arXiv:1308.5454v4. That Section was incomplete and erroneous. This new article fixes and completes that work. For the Proceedings of Operator Algebras, Toeplitz Operators and Related Topics, (OATORT) held in Boca del Rio, Veracruz, Mexico in November, 2018