Algebraic properties of Toeplitz operators on the Dirichlet space |
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Authors: | Young Joo Lee |
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Institution: | Department of Mathematics, Chonnam National University, Gwangju 500-757, Republic of Korea |
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Abstract: | We study some algebraic properties of Toeplitz operators on the Dirichlet space. We first characterize (semi-)commuting Toeplitz operators with harmonic symbols. Next we study the product problem of when product of two Toeplitz operators is another Toeplitz operator. As an application, we show that the zero product of two Toeplitz operators with harmonic symbol has only a trivial solution. Also, the corresponding compact product problem is studied. |
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Keywords: | Toeplitz operator Dirichlet space Products |
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