Note on Köthe Spaces.
Completeness criterion of W. Robertson is generalized. Applications to vector valued sequences and to spaces of linear mappings are given.
A complete isomorphic classification is obtained for Köthe spaces such that ; here χ is the characteristic function of the interval [0,∞), the function κ: ℕ → ℕ repeats its values infinitely many times, and . Any of these spaces has the quasi-equivalence property.