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.
equicontinuous weak*-null sequence in the dual
scientific article; zbMATH DE number 4065657