A Lipschitz estimate for Berezin’s operator calculus

Coburn, L.

doi:10.1090/S0002-9939-04-07476-3

A Lipschitz estimate for Berezin’s operator calculus
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by L. A. Coburn PDF

Proc. Amer. Math. Soc. 133 (2005), 127-131 Request permission

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, $\mathbf {C}^{n}$, 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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