Archiv der Mathematik

, Volume 70, Issue 1, pp 57-65

First online:

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

  • Plamen Borissov DjakovAffiliated withDepartment of Mathematics, Sofia University, BG-1164 Sofia, Bulgaria
  • , Süleyman ÖnalAffiliated withDepartment of Mathematics, Middle East Technical University, TR-06531 Ankara, Turkey
  • , Murat YurdakulAffiliated withDepartment of Mathematics, Middle East Technical University, TR-06531 Ankara, Turkey
  • , Tosun TerzioğluAffiliated withSabanci University, TR-Istanbul, Turkey

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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.