# Sequence Spaces

1. Aug 14, 2008

### olliemath

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. Aug 14, 2008

### morphism

The fact that a separable Banach space is a quotient of $$\ell_1(\mathbb{N})$$ 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.