On quotients of Köthe sequence spaces of infinite order
For a Köthe sequence space \(E=\lambda_\infty(A)\) the authors prove that the following conditions are equivalent: (a) \(E\) is quasinormable. (b) Every quotient of \(E\) satisfies the density condition. (c) Every separable quotient of \(E\) is reflexive. (d) \(E\) satisfies the local Grothendieck property. It is also proved here that \(E\) always satisfies the Grothendieck property (i.e. every \(\sigma(E',E)\)-null sequence is \(\sigma(E',E'')\)-null).
scientific article; zbMATH DE number 938527