On a problem by N. Kalton and the space \(l^p(I)\) (Q949114)

The authors claim to have proved that every infinite-dimensional quasi-Banach space contains a proper closed infinite-dimensional subspace; this is a major open problem in the theory of these spaces. However, their argument is incorrect since it is built on the erroneous assumption that a continuous surjection between dense subspaces of quasi-Banach spaces \(X\) and \(Y\) extends to a continuous surjection between \(X\) and \(Y\) themselves. The paper also contains an incorrect proof of the known fact that \(L_p[0,1]\) is primary for \(0<p<1\).