Commutants of Toeplitz operators with radial symbols on the Fock–Sobolev space

In the setting of the Fock space over the complex plane, Bauer and Lee have recently characterized commutants of Toeplitz operators with radial symbols, under the assumption that symbols have at most polynomial growth at infinity. Their characterization states: If one of the symbols of two commuting...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2014-07, Vol.415 (2), p.779-790
Main Authors: Choe, Boo Rim, Yang, Jongho
Format: Article
Language:English
Subjects:
Commutant
Fock–Sobolev space
Radial symbol
Toeplitz operator
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Summary:In the setting of the Fock space over the complex plane, Bauer and Lee have recently characterized commutants of Toeplitz operators with radial symbols, under the assumption that symbols have at most polynomial growth at infinity. Their characterization states: If one of the symbols of two commuting Toeplitz operators is nonconstant and radial, then the other must be also radial. We extend this result to the Fock–Sobolev spaces.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2014.02.018