Strictly singular operators and isomorphisms of Cartesian products of power series spaces

Abstract.

V. P. Zahariuta, in 1973, used the theory of Fredholm operators to develop a method to classify Cartesian products of locally convex spaces. In this work we modify his method to study the isomorphic classification of Cartesian products of the kind $E_0^p(a)\times E_\infty ^q(b)$ where $1 \leq p,q \le \infty, p \neq q, a = (a_n)_{n=1}^\infty$ and $b = (b_n)_{n=1}^\infty$ are sequences of positive numbers and $E_0^p(a), E_\infty ^q (b)$ are respectively $\ell ^p$-finite and $\ell ^q$-infinite type power series spaces.