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 E0p(a)×E¥ q(b) where 1 £ p,q £ ¥, p ¹ q, a = (an)n=1¥ and b = (bn)n=1¥ are sequences of positive numbers and E0p(a), E¥ q (b) are respectively lp-finite and lq-infinite type power series spaces.