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A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.

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James $\ell_1$-theorem

This question was asked at MSe before but with no answer. I am struggling with the very last estimate in the proof of James' $\ell_1$-theorem. (Please see below an excerpt from Albiac and Kalton's fa …
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