Toeplitz Operators with Bmo Symbols on the Segal-bargmann Space
نویسندگان
چکیده
We show that Zorboska’s criterion for compactness of Toeplitz operators with BMO symbols on the Bergman space of the unit disc holds, by a different proof, for the Segal-Bargmann space of Gaussian square-integrable entire functions on Cn. We establish some basic properties of BMO for p ≥ 1 and complete the characterization of bounded and compact Toeplitz operators with BMO symbols. Via the Bargmann isometry and results of Lo and Englĭs, we also give a compactness criterion for the Gabor-Daubechies “windowed Fourier localization operators” on L2(Rn, dv) when the symbol is in a BMO Sobolev-type space. Finally, we discuss examples of the compactness criterion and counterexamples to the unrestricted application of this criterion for the compactness of Toeplitz operators.
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