, Volume 70, Issue 1, pp 57-65

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

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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.

Received: 18.3.1996; actual version received 16.6.1997.