Characterizations of Bergman space Toeplitz operators with harmonic symbols

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.

• Författare: Anders Olofsson; Louhichi Issam
• Avdelning/ar: Matematik (naturvetenskapliga fakulteten)
• Publiceringsår: 2008
• Språk: Engelska
• Sidor: 1-26
• Publikation/Tidskrift/Serie: Journal für Die Reine und Angewandte Mathematik
• Volym: 2008
• Issue: 617
• Länkar: http://dx.doi.org/10.1515/CRELLE.2008.024
• Dokumenttyp: Artikel i tidskrift
• Förlag: De Gruyter
• Ämne: Mathematics
• Status: Published
• ISBN/ISSN/Övrigt: ISSN: 0075-4102