The existence of a factorized unbounded operator between Fréchet spaces

Abstract

For locally convex spaces X and Y , the continuousOur main result is that the existence of an unbounded operator T between Fréchet spaces E and F which factors through a third Fréchet space G ends up with the fact that the triple (E, G, F ) has an infinite dimensional closed common nuclear Köthe subspace, provided that F has the property (y).