ScholarLens Back to search
2011•Abstract and Applied AnalysisOpen access

Algebraic Properties of Toeplitz Operators on the Polydisk

Bo Zhang, Yanyue Shi, Yufeng Lu

Open full text 4 citations

Abstract

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.

Open-access reader

About this research paper

What this paper is about

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.

Why it matters

OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

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.

Key concepts: Toeplitz matrix, Mathematics, Algebraic number, Rank (graph theory), Algebra over a field, Pure mathematics, Diagonal, Mathematical analysis

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Algebraic Properties of Toeplitz Operators on the Polydisk — Research Paper | ScholarLens