Characterizations of Bergman space Toeplitz operators with harmonic symbols
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Issam Louhichi
Abstract
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.
© Walter de Gruyter Berlin · New York 2008
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- Characterizations of Bergman space Toeplitz operators with harmonic symbols
- A construction of actions on Kirchberg algebras which induce given actions on their K-groups
- Levine's motivic comparison theorem revisited
- Phénomènes de symétrie dans des formes linéaires en polyzêtas
- Motivic decomposition of a compactification of a Merkurjev-Suslin variety
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Articles in the same Issue
- Characterizations of Bergman space Toeplitz operators with harmonic symbols
- A construction of actions on Kirchberg algebras which induce given actions on their K-groups
- Levine's motivic comparison theorem revisited
- Phénomènes de symétrie dans des formes linéaires en polyzêtas
- Motivic decomposition of a compactification of a Merkurjev-Suslin variety
- On period maps that are open embeddings
- T-spectra and Poincaré duality
- The stable mapping class group of simply connected 4-manifolds
