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Transactions of the American Mathematical Society

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A generalization of the Riesz theory of completely continuous transformations


Author: Lawrence M. Graves
Journal: Trans. Amer. Math. Soc. 79 (1955), 141-149
MSC: Primary 46.2X
DOI: https://doi.org/10.1090/S0002-9947-1955-0072438-3
MathSciNet review: 0072438
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References [Enhancements On Off] (What's this?)

  • [1] S. Banach, Théorie des opérations linéaires, 1932.
  • [2] F. Riesz, Über lineare Funktionalgleichungen, Acta Math. vol. 41 (1918) pp. 71-98. MR 1555146
  • [3] T. H. Hildebrandt, Über vollstetige lineare Transformationen, Acta Math. vol. 51 (1928) pp. 311-318. MR 1555265
  • [4] J. Schauder, Über lineare vollstetìge Funktionaloperationen, Studia Mathematica vol. 2 (1930) pp. 183-196.
  • [5] L. Schwartz, Homomorphismes et applications complètement continues, C. R. Acad. Sci. Paris vol. 236 (1953) pp. 2472-2473. This note gives an extension to linear topological spaces of part of Theorem 1 above. MR 0057457 (15:233b)

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DOI: https://doi.org/10.1090/S0002-9947-1955-0072438-3
Article copyright: © Copyright 1955 American Mathematical Society

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