Schwartz spaces and compact holomorphic mappings
Copyright policy )Schwartz spaces and compact holomorphic mappings
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.
- Åbo Akademi University Finland
- DigiZeitschriften Germany
Spaces defined by inductive or projective limits (LB, LF, etc.), equicontinuous weak*-null sequence in the dual, Article, compact holomorphic mappings, 510.mathematics, Geometry and structure of normed linear spaces, Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), quasi-normable locally convex space, Schwartz space, Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
Spaces defined by inductive or projective limits (LB, LF, etc.), equicontinuous weak*-null sequence in the dual, Article, compact holomorphic mappings, 510.mathematics, Geometry and structure of normed linear spaces, Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), quasi-normable locally convex space, Schwartz space, Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
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