In this paper it is proved that the backward shift operator on the Köthe sequence space admits a pair which is not asymptotic, if and only if it has an uncountable invariant -scrambled set for some > 0, if and only if it has an -scrambled subspace for some > 0, if and only if it has an invariant scrambled linear manifold. An analogous result for distributional chaos of type 2 is also obtained.
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