On Köthe spaces
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- by Robert Welland
- Trans. Amer. Math. Soc. 112 (1964), 267-277
- DOI: https://doi.org/10.1090/S0002-9947-1964-0172110-0
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References
- N. Bourbaki, Eléments de mathématique. XV. Première partie: Les structures fondamentales de l’analyse. Livre V: Espaces vectoriels topologiques. Chapitre I: Espaces vectoriels topologiques sur un corps valué. Chapitre II: Ensembles convexes et espaces localement convexes, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1189, Hermann & Cie, Paris, 1953 (French). MR 0054161 —, Intégration, Chapters I-IV, Actualités Sci. Ind., Hermann, Paris, 1952.
- J. L. B. Cooper, Coordinated linear spaces, Proc. London Math. Soc. (3) 3 (1953), 305–327. MR 56823, DOI 10.1112/plms/s3-3.1.305
- Jean Dieudonné, Sur les espaces de Köthe, J. Analyse Math. 1 (1951), 81–115 (French). MR 41347, DOI 10.1007/BF02790084
- Casper Goffman, Completeness in topological vector lattices, Amer. Math. Monthly 66 (1959), 87–92. MR 99584, DOI 10.2307/2310004
- Paul R. Halmos, Measure Theory, D. Van Nostrand Co., Inc., New York, N. Y., 1950. MR 0033869, DOI 10.1007/978-1-4684-9440-2 G. Köthe and O. Toeplitz, Lineare Räume mit unendlichen Koordinaten, J. Reine Angew. Math. 171 (1934), 193-226.
- G. Köthe, Die Stufenräume, eine einfache Klasse linearer vollkommener Räume, Math. Z. 51 (1948), 317–345 (German). MR 27124, DOI 10.1007/BF01181598
- Gottfried Köthe, Neubegründung der Theorie der vollkommenen Räume, Math. Nachr. 4 (1951), 70–80 (German). MR 39912, DOI 10.1002/mana.19500040109
- G. G. Lorentz, Relations between function spaces, Proc. Amer. Math. Soc. 12 (1961), 127–132. MR 123182, DOI 10.1090/S0002-9939-1961-0123182-3
- G. G. Lorentz and D. G. Wertheim, Representation of linear functionals on Köthe spaces, Canad. J. Math. 5 (1953), 568–575. MR 58119, DOI 10.4153/cjm-1953-064-4
- Wilhelmus Anthonius Josephus Luxemburg, Banach function spaces, Technische Hogeschool te Delft, Delft, 1955. Thesis. MR 0072440 A. Zaanen, Linear analysis, Interscience, New York, 1953.
Bibliographic Information
- © Copyright 1964 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 112 (1964), 267-277
- MSC: Primary 46.35
- DOI: https://doi.org/10.1090/S0002-9947-1964-0172110-0
- MathSciNet review: 0172110