Completion of Schwartz Convergence Vector Spaces
Copyright policy )Completion of Schwartz Convergence Vector Spaces
In Math. Nachr. 117, 37-49 (1984; Zbl 0568.46009), we have studied the category of \(L_ eL_ m\)-embedded Schwartz spaces, a category that contains all Hausdorff topological Schwartz spaces as well as all polar bornological Schwartz spaces in the sense of H. Hogbe-Nlend. An \(L_ eL_ M\)-embedded space is a locally convex convergence vector space E for which the canonical mapping into the bidual \(L_ eL_ ME\) is an embedding. Here the dual \(L_ ME\) carries the Marinescu uniform convergence structure. In this note it is shown that the completion of a Schwartz space E in the category of \(L_ eL_ M\)-embedded spaces is linearly homeomorphic with the bidual \(L_ eL_ ME\). The connection between \(L_ eL_ M\)-embedded Schwartz spaces and Hausdorff topological Schwartz spaces is also studied.
- Åbo Akademi University Finland
Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), completion of a Schwartz space, locally convex convergence vector space, canonical mapping into the bidual, Topological linear spaces and related structures, Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.), Spaces defined by inductive or projective limits (LB, LF, etc.), category of \(L_ eL_ m\)-embedded Schwartz spaces, Marinescu uniform convergence structure
Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.), completion of a Schwartz space, locally convex convergence vector space, canonical mapping into the bidual, Topological linear spaces and related structures, Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.), Spaces defined by inductive or projective limits (LB, LF, etc.), category of \(L_ eL_ m\)-embedded Schwartz spaces, Marinescu uniform convergence structure
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