The paper considers the well-known result: if __ is a symmetric Banach space on__ , different from __ up to the equivalent norm, ___ is a compact operator on __ and __ is a rich subspace of __ , then the subspace ___ is also rich. A proof is proposed that does not use the weak convergence of the Rademacher system to zero, which makes it possible to generalize the result to an arbitrary __ -Köté space with an absolutely continuous norm on a space with finite atom-free measure___.

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