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COMPACT OPERATORS AND THE PLURIHARMONIC BEREZIN TRANSFORM

Institut für Mathematik und Informatik, Ernst-Moritz-Arndt-Universität Greifswald, Jahnstrasse 15a, 17487 Greifswald, Germany

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and

KENRO FURUTANI

Department of Mathematics, Faculty of Science and Technology, Science University of Tokyo, Noda, Chiba (278-8510), Japan

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https://doi.org/10.1142/S0129167X08004832Cited by:8 (Source: Crossref)

Abstract

For a series of weighted Bergman spaces over bounded symmetric domains in ℂⁿ, it has been shown by Axler and Zheng [1]; Englis [10] that the compactness of Toeplitz operators with bounded symbols can be characterized via the boundary behavior of its Berezin transform B_a. In case of the pluriharmonic Bergman space, the pluriharmonic Berezin transform B_ph fails to be one-to-one in general and even has non-compact operators in its kernel. From this point of view, perhaps surprisingly we show that via B_ph the same characterization of compactness holds for Toeplitz operators on the pluriharmonic Fock space.

Keywords:

AMSC: 47B35, 32A36, 31C10

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