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Quotients of $ c\sb{0}$ are almost isometric to subspaces of $ c\sb{0}$


Author: Dale E. Alspach
Journal: Proc. Amer. Math. Soc. 76 (1979), 285-288
MSC: Primary 46B25; Secondary 46A45
DOI: https://doi.org/10.1090/S0002-9939-1979-0537089-4
MathSciNet review: 537089
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Abstract: It is shown that for every $ \varepsilon > 0$ and quotient space X of $ {c_0}$ there is a subspace Y of $ {c_0}$ such that the Banach-Mazur distance $ d(X,Y)$ is less than $ 1 + \varepsilon $. This improves a result of Johnson and Zippin.


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

  • [1] N. Dunford and J. T. Schwarz, Linear operators. I: General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958.
  • [2] W. B. Johnson and M. Zippin, Subspaces of $ {(\Sigma {G_n})_{{l_p}}}$ and $ {(\Sigma {G_n})_{{c_0}}}$, Israel J. Math. 17 (1974), 50-55. MR 0358296 (50:10762)
  • [3] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces, Lecture Notes in Math., vol. 338, Springer-Verlag, Berlin and New York, 1973. MR 0415253 (54:3344)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0537089-4
Keywords: Quotient space, almost isometric
Article copyright: © Copyright 1979 American Mathematical Society

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