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Sequence Spaces

  1. Aug 14, 2008 #1
    I'm currently studying Intro to Tensor Products of Banach Spaces by Ryan. In it he makes the off-hand remark

    Is it? Does anyone know what this result is called, or where I can find a proof of it?
    Cheers in advance - O
     
  2. jcsd
  3. Aug 14, 2008 #2

    morphism

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    The fact that a separable Banach space is a quotient of [tex]\ell_1(\mathbb{N})[/tex] is pretty well-known, and a proof can be found for example on pages 103-104 of
    Morrison, Functional Analysis: An Introduction to Banach Space Theory. Wiley-Interscience, 2000.

    I just scanned the proof and I think you can easily modify it to get the result you want. Or you can try Lindenstrauss-Tzafriri, Dunford-Schwarz or Megginson to see if they have a proof of the general result.
     
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