A note on extensions of Pełczyński's decomposition method in Banach spaces
Elói Medina Galego (2007)
Studia Mathematica
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Let X,Y,A and B be Banach spaces such that X is isomorphic to Y ⊕ A and Y is isomorphic to X ⊕ B. In 1996, W. T. Gowers solved the Schroeder-Bernstein problem for Banach spaces by showing that X is not necessarily isomorphic to Y. In the present paper, we give a necessary and sufficient condition on sextuples (p,q,r,s,u,v) in ℕ with p + q ≥ 2, r + s ≥ 1 and u, v ∈ ℕ* for X to be isomorphic to Y whenever these spaces satisfy the following decomposition scheme: ⎧ , ⎨ ⎩ . Namely, Ω =...