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Subspaces and quotient spaces of\((\Sigma G_n )_{l_p } \) and\((\Sigma G_n )_{c_0 } \)

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Abstract

Let (G n) be a sequence which is dense (in the sense of the Banach-Mazur distance coefficient) in the class of all finite dimensional Banach spaces. Set\(C_p = (\Sigma G_n )_{l_p } (1< p< \infty ) = (\Sigma G_n )_{c_0 } \). It is shown that a Banach spaceX is isomorphic to a subspace ofC p (1<p≦∞) if and only ifX is isomorphic to a quotient space ofC p.

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References

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Both authors were supported in part by NSF GP-33578.

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Johnson, W.B., Zippin, M. Subspaces and quotient spaces of\((\Sigma G_n )_{l_p } \) and\((\Sigma G_n )_{c_0 } \) . Israel J. Math. 17, 50–55 (1974). https://doi.org/10.1007/BF02756824

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  • DOI: https://doi.org/10.1007/BF02756824

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