Algebraic Properties of Toeplitz Operators on the Polydisk | Zendy

Bo Zhang | Zendy; Yanyue Shi | Zendy; Yufeng Lu | Zendy

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Algebraic Properties of Toeplitz Operators on the Polydisk

Author(s) -

Bo Zhang,

Yanyue Shi,

Yufeng Lu

Publication year - 2011

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2011/962313

Subject(s) - toeplitz matrix , mathematics , algebraic number , rank (graph theory) , algebra over a field , pure mathematics , diagonal , mathematical analysis , combinatorics , geometry

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

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