Hilbert-Schmidt differences of composition operators on the Bergman space (Q658353)
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scientific article; zbMATH DE number 5996714
| Language | Label | Description | Also known as |
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| English | Hilbert-Schmidt differences of composition operators on the Bergman space |
scientific article; zbMATH DE number 5996714 |
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Hilbert-Schmidt differences of composition operators on the Bergman space (English)
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12 January 2012
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The present paper gives a nice formula for the Hilbert-Schmidt norm of a difference of two composition operators on weighted Bergman spaces of the unit disk. The paper also shows that any linear combination of two composition operators cannot be Hilbert-Schmidt, except in trivial cases, unless the combination is a difference. Using the Hilbert-Schmidt norm topology, some topological properties of the space of composition operators are also studied.
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composition operator
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weighted Bergman space
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Hilbert-Schmidt operator
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