A characterization of absolutely summing operators by means of McShane integrable functions (Q1827069)
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scientific article; zbMATH DE number 2082129
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A characterization of absolutely summing operators by means of McShane integrable functions |
scientific article; zbMATH DE number 2082129 |
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A characterization of absolutely summing operators by means of McShane integrable functions (English)
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6 August 2004
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The basic definition of an absolutely summing operator may be viewed as a relationship between certain ``strong'' and ``weak'' integrals of vector-valued functions with finitely many values. This property has various counterparts expressed in terms of more general measurable vector-valued functions. The paper under review describes a variation of this theme: an operator is absolutely summing if and only if it takes McShane integrable functions to Bochner integrable functions.
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absolutely summing operator
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McShane integral
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Bochner integral
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Pettis integral
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