Abstract
A twisted sum of (topological vector) spaces Y Y and Z Z is a space X X with a subspace Y 1 {Y_1} isomorphic to Y Y for which X / Y 1 X/{Y_1} is isomorphic to Z Z . It splits if Y 1 {Y_1} is complemented. It is proved that every twisted sum of a Banach space Y Y and a nuclear space Z Z splits. Köthe sequence spaces Z Z for which this holds are characterized. Every locally convex twisted sum of a nuclear Fréchet space Y Y and a Banach space Z Z splits too. If Z Z is superreflexive, then the local convexity assumption on the twisted sum may be omitted. Other results of this kind on Köthe sequence spaces are obtained.
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