Exposé on a paper of Dronov and Kaplitzkii

Abstract

Dronov and Kaplitzki showed that every complemented subspace of a nuclear Köthe space E with a regular basis of type ($d_1$) has a basis so, in particular, solving the long standing problem whether any complemented subspace of the space (s) of rapidly decreasing sequences has a basis. We present a slightly modified version of their proof which shows that the range of every closed-range operator in $E$ has a basis