A characterization of Schwartz spaces
Copyright policy )A characterization of Schwartz spaces
It is proved that a locally convex space E is a Schwartz space iff it is quasi-normable and every equicontinuous weak* convergent sequence in the dual of E is strongly convergent. The result depends on the characterization of compact operators between Banach spaces as precisely those which are representable as the product of three limited operators. Several applications are given. For example, if E is quasi-normable and the space of compact mappings \(K_{\beta}(E,c_ 0)\) is a complemented subspace of \(L_{\beta}(E,c_ 0)\), then E is Schwartz.
- DigiZeitschriften Germany
- Åbo Akademi University Finland
characterization of compact operators between Banach spaces, limited operators, locally convex space, Spaces defined by inductive or projective limits (LB, LF, etc.), Article, quasi-normable, 510.mathematics, Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), equicontinuous weak* convergent sequence in the dual, Schwartz space, complemented subspace, Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
characterization of compact operators between Banach spaces, limited operators, locally convex space, Spaces defined by inductive or projective limits (LB, LF, etc.), Article, quasi-normable, 510.mathematics, Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), equicontinuous weak* convergent sequence in the dual, Schwartz space, complemented subspace, Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
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