Archiv der Mathematik

, Volume 85, Issue 5, pp 433–439 | Cite as

On extensions of Pełczyński’s decomposition method in Banach spaces

Original Paper


Let X and Y be Banach spaces such that each of them is isomorphic to a complemented subspace of the other. In 1996, W. T. Gowers solved the Schroeder-Bernstein Problem for Banach spaces by showing that X is not necessarily isomorphic to Y. In this paper, we give suitable conditions on finite sums of X and Y to yield that X m is isomorphic to Y n for some \(m,n \in \mathbb{N}^{*} .\) In other words, we obtain some extensions of the well-known Pełczyński decomposition method in Banach spaces. In order to do this, we introduce the notion of Nearly Schroeder-Bernstein Quadruples for Banach spaces and pose a Conjecture to characterise them.

Mathematics Subject Classification (2000).

Primary 46B03 46B20 


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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Department of Mathematics - IMEUniversity of São PauloSão PauloBrazil

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