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Centralizers of Toeplitz operators with polynomial symbols

In this note we describe centralizers of Toeplitz operators with polynomial symbols on the Bergman space. As a consequence it is shown that if an element of the norm closed algebra generated by all Toeplitz operators commutes with a Toeplitz operator of a noncon- stant polynomial, then this element is a Toeplitz operator of a bounded holomorphic function.

preprint2010arXivOpen access
Akaki Tikaradze
math.FA
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Akaki Tikaradze

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