On the Berezin-Toeplitz calculus

Author:
L. A. Coburn

Journal:
Proc. Amer. Math. Soc. **129** (2001), 3331-3338

MSC (2000):
Primary 47B35; Secondary 47B32

Published electronically:
March 29, 2001

MathSciNet review:
1845010

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the problem of composing Berezin-Toeplitz operators on the Hilbert space of Gaussian square-integrable entire functions on complex -space, . For several interesting algebras of functions on , we have for all in the algebra, where is the Berezin-Toeplitz operator associated with and is a ``twisted'' associative product on the algebra of functions. On the other hand, there is a function for which is bounded but for any .

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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

DOI:
http://dx.doi.org/10.1090/S0002-9939-01-05917-2

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

Article copyright:
© Copyright 2001
American Mathematical Society