Some summability properties of operators on a separable Banach space (Q1263057)
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scientific article; zbMATH DE number 4126110
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some summability properties of operators on a separable Banach space |
scientific article; zbMATH DE number 4126110 |
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Some summability properties of operators on a separable Banach space (English)
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1990
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It is a well known fact that operators on a separable Hilbert space H giving norm-summability on an orthonormal basis have to be nuclear (Holub 1972) and operators giving summability on an orthonormal basis must be Hilbert-Schmidt. In former papers the author characterizes all the sequences of H that in this respect behave as orthonormal basis, and in the present paper those results are in some way, generalized to a separable Banach space.
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compact operator
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nuclear operator
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absolutely summable sequence
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norm- summability on an orthonormal basis
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Hilbert-Schmidt
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