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Algebraic Properties of Toeplitz Operators on the Harmonic Dirichlet Space |
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| Authors: | Yong Chen Young Joo Lee Quang Dieu Nguyen |
| Institution: | 1.College of Mathematics, Physics and Information Engineering,Zhejiang Normal University,Jinhua,People’s Republic of China;2.School of Mathematical Sciences,Fudan University,Shanghai,People’s Republic of China;3.Department of Mathematics,Chonnam National University,Gwangju,Korea;4.Department of Mathematics,Ha Noi National University of Education,Ha Noi,Vietnam |
| Abstract: | We study some algebraic properties of Toeplitz operators on the harmonic Dirichlet space of the unit disk. We first give a characterization for boundedness of Toeplitz operators. Next we characterize commuting Toeplitz operators. Also, we study the product problem of when product of two Toeplitz operators is another Toeplitz operator. The corresponding problems for compactness are also studied. |
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