conditions on l(A),l(A)  X l'(A) is isomorphic to l(A) l'(A).We use this result to generalize 

Valdivia's decomposition method.More precisely we prove the following: If there is a local imbedding i 

from l(A)l'(A) , then E has a complemented subspace isomorphic to l(A)l'(A). 

We used our generalized version to show that SS'  is isomorphic to O_M.Further we generalized 

a result of  Terzioğlu and we gave the required examples to show that we have a real generalization. 

Key words: Nuclear Spaces, Tensor Products, Local Imbeddings, Decomposition Theorems.