Geodesic
AN ARITHMETICAL CHARACTERIZATION OF DECOMPOSITION METHODS IN BANACH SPACES VIA SUPPLEMENTED SUBSPACES
Glasgow mathematical journal, Tome 47 (2005) no. 3, pp. 489-500

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DOI

Let X and Y be Banach spaces such that each one 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 X, Y, the supplemented subspaces of Y in X and of X in Y to yield that X is isomorphic to Y. In other words, we obtain generalizations of Pełczyński's decomposition method via supplemented subspaces. In order to determine all the possible generalizations, we introduce the notion of Mixed Schroeder-Bernstein Quadruples for Banach spaces. Then, we use some Banach spaces constructed by W. T. Gowers and B. Maurey in 1997 to characterize them.
DOI : 10.1017/S0017089505002727
Mots-clés : 46B03, 46B20 
GALEGO, ELÓI MEDINA. AN ARITHMETICAL CHARACTERIZATION OF DECOMPOSITION METHODS IN BANACH SPACES VIA SUPPLEMENTED SUBSPACES. Glasgow mathematical journal, Tome 47 (2005) no. 3, pp. 489-500. doi: 10.1017/S0017089505002727
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     title = {AN {ARITHMETICAL} {CHARACTERIZATION} {OF} {DECOMPOSITION} {METHODS} {IN} {BANACH} {SPACES} {VIA} {SUPPLEMENTED} {SUBSPACES}},
     journal = {Glasgow mathematical journal},
     pages = {489--500},
     year = {2005},
     volume = {47},
     number = {3},
     doi = {10.1017/S0017089505002727},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089505002727/}
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