Algebraic Properties of Toeplitz Operators on the Polydisk

Algebraic Properties of Toeplitz Operators on the Polydisk

We discuss some algebraic properties of Toeplitz operators on the Bergman space of the polydisk Dn. Firstly, we introduce Toeplitz operators with quasihomogeneous symbols and property (P). Secondly, we study commutativity of certain quasihomogeneous Toeplitz operators and commutators of diagonal Toe...

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Veröffentlicht in:Abstract and Applied Analysis 2011-01, Vol.2011 (2011), p.4212-4229
Hauptverfasser: Zhang, Bo, Shi, Yanyue, Lu, Yufeng
Format: Artikel
Sprache:eng
Schlagworte:
Operator theory
Vector spaces
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Zusammenfassung:We discuss some algebraic properties of Toeplitz operators on the Bergman space of the polydisk Dn. Firstly, we introduce Toeplitz operators with quasihomogeneous symbols and property (P). Secondly, we study commutativity of certain quasihomogeneous Toeplitz operators and commutators of diagonal Toeplitz operators. Thirdly, we discuss finite rank semicommutators and commutators of Toeplitz operators with quasihomogeneous symbols. Finally, we solve the finite rank product problem for Toeplitz operators on the polydisk.
ISSN:1085-3375
1687-0409
DOI:10.1155/2011/962313