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Let K be a non-archimedean valued field whose valuation is complete and nontrivial. It is shown that l∞ is complemented in any polar K-Banach space (Theorem 1.2) which opens the way for various descriptions of complemented subspaces of l∞ (Theorem 2.3).

The complementation property of ℓ∞ in p-adic banach spaces