A barrelled space without a basis
Author:
N. J. Kalton
Journal:
Proc. Amer. Math. Soc. 26 (1970), 465-466
MSC:
Primary 46.01
DOI:
https://doi.org/10.1090/S0002-9939-1970-0273353-6
MathSciNet review:
0273353
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Abstract | References | Similar Articles | Additional Information
Abstract: An example is given of a separable, barrelled, nuclear, bornological Ptak space which has no Schauder basis.
- James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606
- N. Kalton, Schauder decompositions and completeness, Bull. London Math. Soc. 2 (1970), 34–36. MR 259547, DOI https://doi.org/10.1112/blms/2.1.34
- Gottfried Köthe, Topologische lineare Räume. I, Die Grundlehren der mathematischen Wissenschaften, Bd. 107, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960 (German). MR 0130551
- Helmut H. Schaefer, Topological vector spaces, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1966. MR 0193469
- Ivan Singer, On the basis problem in topological linear spaces, Rev. Roumaine Math. Pures Appl. 10 (1965), 453–457. MR 194875
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Additional Information
Keywords:
Locally convex spaces,
basis,
separable,
barrelled,
nuclear
Article copyright:
© Copyright 1970
American Mathematical Society