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Short proof of Sobczyk's theorem


Author: William A. Veech
Journal: Proc. Amer. Math. Soc. 28 (1971), 627-628
MSC: Primary 46.10
DOI: https://doi.org/10.1090/S0002-9939-1971-0275122-0
MathSciNet review: 0275122
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Abstract: A new proof is given of Sobczyk's Theorem, which asserts that $ {c_0}$ is complemented in any separable Banach space which contains it (isomorphically) as a closed subspace.


References [Enhancements On Off] (What's this?)

  • [1] N. Dunford and J. T. Schwartz, Linear operators. I: General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR 22 #8302. MR 0117523 (22:8302)
  • [2] A. Sobczyk, Projection of the space $ (m)$ on its subspace $ ({c_0})$, Bull. Amer. Math. Soc. 47 (1941), 938-947. MR 3, 205. MR 0005777 (3:205f)
  • [3] G. Köthe, Über einen Satz von Sobczyk, An. Fac. Ci. Univ. Porto 49 (1966), 281-286. MR 37 #3322. MR 0227738 (37:3322)
  • [4] S. Goldberg, On Sobczyk's projection theorem, Amer. Math. Monthly 76 (1969), 523-526. MR 39 #6054. MR 0244740 (39:6054)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0275122-0
Keywords: Separable Banach space, projection, weakly compactly generated Banach space
Article copyright: © Copyright 1971 American Mathematical Society

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