The Cesàro operator on the Bergman space \( A^2(\mathbb D)\) (Q1614940)
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scientific article; zbMATH DE number 1798892
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Cesàro operator on the Bergman space \( A^2(\mathbb D)\) |
scientific article; zbMATH DE number 1798892 |
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The Cesàro operator on the Bergman space \( A^2(\mathbb D)\) (English)
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10 September 2002
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The Cesàro operator is shown to be subdecomposable on the Bergman spaces \(A^p (\mathbb D)\) for \(p \geqq 2\), extending a result of the authors to the case that \(p<4\). For \(A^2 (\mathbb D)\), we show that Cesàro operator is in fact subscalar, but in contrast to the situation in the Hardy space, \(C _{A^2}\) fails to be hyponormal.
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Cesàro operator
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subdecomposable
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subscalar
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Hardy space
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hyponormal
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0.9456445
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0.91468036
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