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- W2116798162 abstract "Let X be a completely regular Hausdorff space and = (vn) be a decreasing sequence of strictly positive continuous functions on X. Let E be a non–normable Fréchet space. It is proved that the weighted inductive limit C(X, E) of spaces of E–valued continuous functions is regular if, and only if, it satisfies condition (M) of Retakh (and, in particular, it is complete). As a consequence, we obtain a positive answer to an open problem of Bierstedt and Bonet. It is also proved that, if C(X, E) = C(X, E) algebraically and X is a locally compact space, the identity C(X, E) = C(X, E) holds topologically if, and only if, the pair (, E) satisfies condition (S2)* of Vogt." @default.
- W2116798162 created "2016-06-24" @default.
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- W2116798162 date "2000-08-01" @default.
- W2116798162 modified "2023-09-25" @default.
- W2116798162 title "On Completeness and Projective Descriptions of Weighted Inductive Limits of Spaces of Fréchet-Valued Continuous Functions" @default.
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- W2116798162 doi "https://doi.org/10.1002/1522-2616(200008)216:1<5::aid-mana5>3.0.co;2-k" @default.
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