Abstract: Let T be an unbounded, continuous, linear operator from Frechet space E into Frechet space 

F and suppose F satisfies the condition which is called (y). It is proved that E and F have a common 

quotient which is nuclear, has a basis and a continuous norm and it can be factored through T. By using 

this result, it is also proved that Frechet spaces which have nuclear quotients with a basis and a 

continuous norm are those Frechet spaces which do not satisfy the condition (b).