Basic sequences in some regular Köthe spaces

In this paper (closed, linear) subspaces of nuclear Köthe spaces are investigated. This has been the topic of various papers by E. Dubinsky, D. Vogt, M. Alpseymen etc. We give complete characterizations for subspaces with basis of unstable Köthe spaces of type D₁, in particular unstable L_f (Drafilev) spaces of type d₁, and regular subspaces of L_f spaces of infinite type without any assumptions on the defining exponent sequence. The method used depends on applying a stability theorem on embeddings of L. Schwartz [17] and the Hall-Koenig theorem [10] on selection of distinct representatives as well as some construction methods of E. Dubinsky [9].