Toeplitz operators on the weighted pluriharmonic Bergman space with radial symbols (Q642694)

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scientific article; zbMATH DE number 5964383
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Toeplitz operators on the weighted pluriharmonic Bergman space with radial symbols
scientific article; zbMATH DE number 5964383

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    Toeplitz operators on the weighted pluriharmonic Bergman space with radial symbols (English)
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    27 October 2011
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    Summary: We construct an operator \(R\) whose restriction onto the weighted pluriharmonic Bergman Space \(b^2_\mu(\mathbb B^n)\) is an isometric isomorphism between \(b^2_{\mu}(\mathbb B^n)\) and \(l^{\sharp}_2\). Furthermore, using the operator \(R\) we prove that each Toeplitz operator \(T_a\) with radial symbols is unitary equivalent to the multiplication operator \(\gamma_{a,\mu}I\). Also it turns out that the Wick function of a Toeplitz operator with radial symbol gives complete information about the operator, providing its spectral decomposition.
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    weighted pluriharmonic Bergman space
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