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Let $X$ be a Banach space with an unconditional basis $(x_{n})_{n}$.

Question. If $X$ contains a subspace isomorphic to $l_{1}$, does $(x_{n})_{n}$ admit a block basic sequence equivalent to the unit vector basis of $l_{1}$ ?

I do not know whether the question has already existed as a known result. But a self-contained proof is preferred.

Thank you.

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Yes. This result of R. C. James can be found in standard references. See, for example, Theorem 3.3.1 in the book by Albiac and Kalton.

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