On Pelczynski’s Problem

Abstract

In 1970 Studia Mathematica published unsolved problems posed by some of the most distinguished mathematicians. Pelczynski asked, whether complemented subspaces of a nuclear Frechet space with basis have a basis [18]. In view of Dynin-Mitiagin’s absolute basis theorem [19] this problem is equivalent to the question, whether complemented subspaces of nuclear Kothe spaces are again Kothe spaces.