Quotients of $c_{0}$ are almost isometric to subspaces of $c_{0}$
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- by Dale E. Alspach PDF
- Proc. Amer. Math. Soc. 76 (1979), 285-288 Request permission
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
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N. Dunford and J. T. Schwarz, Linear operators. I: General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958.
- W. B. Johnson and M. Zippin, Subspaces and quotient spaces of $(\sum G_{n})_{l_{p}}$ and $(\sum G_{n})_{c_{0}}$, Israel J. Math. 17 (1974), 50–55. MR 358296, DOI 10.1007/BF02756824
- Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces, Lecture Notes in Mathematics, Vol. 338, Springer-Verlag, Berlin-New York, 1973. MR 0415253
Additional Information
- © Copyright 1979 American Mathematical Society
- 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