Abstract
We show that the ℓ 1 -product ( X ⊕ X ⊕ ⋯ ⊕ X ⊕ ⋯ ) 1 has a unique unconditional basis up to permutation for a wide class of nonlocally convex quasi-Banach spaces X, even without knowing whether X has a unique unconditional basis or not.
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