A note on vanishing of the functor ext1 for Köthe spaces

Abstract

In this note we study the relationship between the vanishing of Ext1(λ(A), λ(A)) and the existence of a regular basis in the Köthe space λ(A). We construct an example of a nuclear Köthe space λ(A) with no regular basis and such that Ext1(λ(A), λ(A))=0. Then we show that for some classes of Köthe spaces λ(A), the vanishing of Ext1(λ(A), λ(A)) yields a regular basis for λ(A). © 1991 Springer-Verlag.