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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the Berezin-Toeplitz calculus
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by L. A. Coburn PDF
Proc. Amer. Math. Soc. 129 (2001), 3331-3338 Request permission

Abstract:

We consider the problem of composing Berezin-Toeplitz operators on the Hilbert space of Gaussian square-integrable entire functions on complex $n$-space, $\mathbf {C}^n$. For several interesting algebras of functions on $\mathbf {C}^n$, we have $T_\varphi T_\psi =T_{\varphi \diamond \psi }$ for all $\varphi ,\psi$ in the algebra, where $T_\varphi$ is the Berezin-Toeplitz operator associated with $\varphi$ and $\varphi \diamond \psi$ is a “twisted” associative product on the algebra of functions. On the other hand, there is a $C^\infty$ function $\varphi$ for which $T_\varphi$ is bounded but $T_\varphi T_\varphi \neq T_\psi$ for any $\psi$.
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Additional Information
  • L. A. Coburn
  • Affiliation: Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260
  • Email: lcoburn@acsu.buffalo.edu
  • Received by editor(s): December 21, 1999
  • Received by editor(s) in revised form: March 21, 2000
  • Published electronically: March 29, 2001
  • Additional Notes: The author’s research was supported by a grant of the NSF and a visiting membership in the Erwin Schrödinger Institute.
  • Communicated by: Joseph A. Ball
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 3331-3338
  • MSC (2000): Primary 47B35; Secondary 47B32
  • DOI: https://doi.org/10.1090/S0002-9939-01-05917-2
  • MathSciNet review: 1845010