Schwartz spaces and compact holomorphic mappings (Q1107788)
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scientific article; zbMATH DE number 4065657
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Schwartz spaces and compact holomorphic mappings |
scientific article; zbMATH DE number 4065657 |
Statements
Schwartz spaces and compact holomorphic mappings (English)
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1988
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Let E be a quasi-normable locally convex space. The following statements are proved equivalent: (a) E is a Schwartz space; (b) Every equicontinuous weak*-null sequence in the dual of E is strongly null; (c) Every continuous linear mapping of E into \(c_ 0\) is compact; (d) Every holomorphic mapping of E into \(c_ 0\) is compact.
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compact holomorphic mappings
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quasi-normable locally convex space
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Schwartz space
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equicontinuous weak*-null sequence in the dual
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