On twisted Fréchet and (LB)-spaces

Abstract

Abstract.We study twisted Fréchet spaces as well as twisted (LZJ)-spaces. We prove that a twisted space can have a nontwisted dual and that twisted spaces of a special class cannot be complemented in nontwisted spaces. We also give new examples of twisted spaces.

Basic and quasibasic subspaces of adjoint Banach spaces

“…Proof. It is known [MM1,p. 149] that in order to prove Theorem 1 it is sufficient to find a sequence {F n } ∞ n=1 of Banach spaces satisfying the following conditions.…”