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Zippin’s Embedding Theorem

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1993)

Abstract

A deep result of Per Enflo [E] asserts that there exists a separable Banach space without a Schauder basis. On the other hand, by Theorem 1.8, every separable Banach space embeds into a Banach space with a Schauder basis. An old problem in Banach Space Theory (see [LT, Problem 1.b.16]) asked whether every space X with separable dual is isomorphic to a subspace of a space Y with a shrinking Schauder basis.

Keywords

  • Banach Space
  • Separable Banach Space
  • Isomorphic Copy
  • Open Subset Versus
  • General Topological Space

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Correspondence to Pandelis Dodos .

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© 2010 Springer-Verlag Berlin Heidelberg

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Dodos, P. (2010). Zippin’s Embedding Theorem. In: Banach Spaces and Descriptive Set Theory: Selected Topics. Lecture Notes in Mathematics(), vol 1993. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12153-1_5

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