Direct Products of Normed Linear Spaces
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 769-773
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In this paper we shall study properties of a locally convex space (l.c.s.) which guarantee that it is a direct product of normed linear spaces or Banach spaces. The conditions will be given both as properties of the original space itself and as properties of the dual, and will take the form of a completeness condition and the existence of sub-basic sets of pseudo-norms with certain properties (a set of pseudo-norms is basic if the set of unit balls of its members is a base of neighbourhoods of 0.
Jones, William B. Direct Products of Normed Linear Spaces. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 769-773. doi: 10.4153/CJM-1967-071-5
@article{10_4153_CJM_1967_071_5,
author = {Jones, William B.},
title = {Direct {Products} of {Normed} {Linear} {Spaces}},
journal = {Canadian journal of mathematics},
pages = {769--773},
year = {1967},
volume = {19},
number = {1},
doi = {10.4153/CJM-1967-071-5},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1967-071-5/}
}
[1] 1. Bourbaki, N., Espaces vectoriels topologiques (Paris, 1955). Chap. 111—V. Google Scholar
[2] 2. Jones, W. B., Duality and types of completeness in locally convex spaces, Pacific J. Math., 18 (1966), 525–544. Google Scholar
[3] 3. Jones, W. B., A locally convex topology for spaces of holomorphic functions, to appear in Math. Ann. Google Scholar
[4] 4. Köthe, G., Topologische lineare Raurne, Vol. 1 (Berlin, 1960). Google Scholar
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