NULL SEQUENCES IN COECHELON SPACES

We prove that for any Kothe matrices a and b if T : lambda(1)(a) --> l ambda(0)(b) maps bounded sets into relatively compact sets, then T fac torizes through a Frechet Montel space. This is a consequence of a giv en description of those compact subsets in a coechelon space k(infinit y)(upsilon) of type infinity which are contained in an absolutely conv ex hull of a null sequence. An example of a compact set which is not o f that form is given.