ABSTRACT
J. A. LOPEZ MOLINA*, F. MARTfNEZ-GIMENEZ, M. J. RIVERA*, E. A. SANCHEZ PEREZ E. T. S. Ingenieros Agr6nomos, Camino de Vera, 46072 Valencia, Spain
INTRODUCTION
In several previous papers (see [9], [10]), some of the authors have characterized pairs ( £ , F) of locally convex spaces of some usual concrete classes such that every T e C ( E % F) is a Montel map. On this communication we solve the same problem in the case that E, F are certain interpolation spaces (A.^°(A), \ Px (B))e , 1 < po < p \ , q < oo, 0 < 0 < 1, (defined by the method of Goulaouic [6]) of echelon Kothe sequence spaces. The key of our method is the alternative description of (k po(A), A/1 (B))e q (based on the previous work of Freitag [5]) as a projective limit of general Lorentz sequence spaces de fined on the set N of natural numbers with an arbitrary measure. It is significative to note that these spaces are not step spaces in the sense of Dubinsky [4] (see below) and hence his results can not be applied to projective limits of them. In particular we need to give a characterization of the spaces (k Po(A), k Pl(B))$ q which are Montel and this is done in the sequel.
