In this thesis ; we studied a modification of the operator method of V.P. Zahariuta forisomorphic classification of cartesian products of locally convex spaces. As an example we consider cartesian products of  l p- finite and l q- infinite type powerseries spaces. In addition, we studied some consequences of the modification in specific cases.

Keywords: Compact, Bounded, Strictly Singular Operators, Power Series Spaces, Montel, Schwartz, Nuclear Spaces, Isomorphism of Cartesian Products.