An Embedding Theorem for Separable Locally Convex Spaces
Canadian mathematical bulletin, Tome 14 (1971) no. 1, pp. 119-120
Voir la notice de l'article provenant de la source Cambridge University Press
A well-known embedding theorem of Banach and Mazur [1, p. 185] states that every separable Banach space is isometrically isomorphic to a subspace of C[0, 1], establishing C[0, 1] as a universal separable Banach space. The embedding theorem one encounters in a course in topological vector spaces states that every Hausdorff locally convex space (l.c.s.) is topologically isomorphic to a subspace of a product of Banach spaces.
Lohman, Robert H. An Embedding Theorem for Separable Locally Convex Spaces. Canadian mathematical bulletin, Tome 14 (1971) no. 1, pp. 119-120. doi: 10.4153/CMB-1971-023-1
@article{10_4153_CMB_1971_023_1,
author = {Lohman, Robert H.},
title = {An {Embedding} {Theorem} for {Separable} {Locally} {Convex} {Spaces}},
journal = {Canadian mathematical bulletin},
pages = {119--120},
year = {1971},
volume = {14},
number = {1},
doi = {10.4153/CMB-1971-023-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-023-1/}
}
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