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Banach spaces complemented in each other without isomorphic finite sums

Galego E. M.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

Vol. 50, no 1

1-9

We show that the first solution of W.T. Gowers to the Schroeder-Bernstein problem for Banach spaces (unpublished) also provides the first example of two Banach spaces Z and W such that each of them is isomorphic to a complemented subspace of the other, but [Z sup m] is not isomorphic to [W sup n] for every m, n [belongs to] N*.