Proceedings of the American Mathematical Society

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



A Lipschitz estimate for Berezin's operator calculus

Author: L. A. Coburn
Journal: Proc. Amer. Math. Soc. 133 (2005), 127-131
MSC (2000): Primary 47B32; Secondary 32A36
Published electronically: August 20, 2004
MathSciNet review: 2085161
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Abstract: F. A. Berezin introduced a general ``symbol calculus" for linear operators on reproducing kernel Hilbert spaces. For the particular Hilbert space of Gaussian square-integrable entire functions on complex $n$-space, ${\text{\bf C}}^{n}$, we obtain Lipschitz estimates for the Berezin symbols of arbitrary bounded operators. Additional properties of the Berezin symbol and extensions to more general reproducing kernel Hilbert spaces are discussed.

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L. A. Coburn
Affiliation: Department of Mathematics, SUNY at Buffalo, Buffalo, New York 14260

Received by editor(s): July 8, 2003
Received by editor(s) in revised form: August 15, 2003, and September 5, 2003
Published electronically: August 20, 2004
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2004 American Mathematical Society