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Characterizations of Bergman space Toeplitz operators with harmonic symbols

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Author

Summary, in English

It is well-known that Toeplitz operators on the Hardy space of the unit disc are characterized by the equality , where S1 is the Hardy shift operator. In this paper we give a generalized equality of this type which characterizes Toeplitz operators with harmonic symbols in a class of standard weighted Bergman spaces of the unit disc containing the Hardy space and the unweighted Bergman space. The operators satisfying this equality are also naturally described using a slightly extended form of the Sz.-Nagy-Foias functional calculus for contractions. This leads us to consider Toeplitz operators as integrals of naturally associated positive operator measures in order to take properties of balayage into account.

Publishing year

2008

Language

English

Pages

1-26

Publication/Series

Journal für Die Reine und Angewandte Mathematik

Volume

2008

Issue

617

Document type

Journal article

Publisher

De Gruyter

Topic

  • Mathematics

Status

Published

ISBN/ISSN/Other

  • ISSN: 0075-4102