Universal Kothe sequence spaces

A characterization is given for the Kothe matrices B such that the Kothe sequence space lambda(p)(B), with p is an element of [1, infinity] boolean OR {0}, contains all Kothe sequence spaces of order p as subspaces. It follows that the class of Kb;the sequence spaces of order p has a universal element which is quasinormable. In particular, there is a quasinormable space lambda(1)(Q) (respectively, lambda(0)(Q)) which contains every nuclear Frechet space with basis (respectively, every countably normed Frechet Schwartz space). Only Frechet spaces with continuous norm are considered in this note.