SOME RESULTS ON SOLVABILITY OF ORDINARY LINEAR DIFFERENTIAL EQUATIONS IN LOCALLY CONVEX SPACES

Abstract

Let be the class of sequentially complete locally convex spaces such that an existence theorem holds for the linear Cauchy problem , , with respect to functions . It is proved that if , then for an arbitrary set . It is also proved that a topological product of infinitely many infinite-dimensional Frechet spaces, each not isomorphic to , does not belong to .