Banach spaces complemented in each other without isomorphic finite sums

• Autorzy: Galego E. M.
• Języki publikacji: EN

Abstrakty

EN

We show that the first solution of W.T. Gowers to the Schroeder-Bernstein problem for Banach spaces (unpublished) also provides the first example of two Banach spaces Z and W such that each of them is isomorphic to a complemented subspace of the other, but [Z sup m] is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*.

Słowa kluczowe

EN

Pełczynski's decomposition method; Schroeder-Bernstein problem

PL

metoda rozkładu Pełczyńskiego; zagadnienie Schroedera-Bernsteina

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2002
• Tom: Vol. 50, no 1
• Strony: 1--9
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Galego E. M.

Bibliografia

• [1] W. T. Gowers, A solution to the Schroeder-Bernstein problem for Banach space, Preliminary version (unpublished).
• [2] W. T. Gowers, A solution to the Schroeder-Bernstein problem for Banach space, Bull. London Math. Soc., 28 (1996) 297-304.
• [3] W. T. Gowers, B. Maurey, The unconditional basie sequence problem, J. Amer. Math. Soc., 6 (1993) 851-874.
• [4] W. T. Gowers, B. Maurey, Banach spaces with small spaces of operators, Math. Ann., 307 (1997) 543-568.
• [5] J. Lindenstrauss, L. Tzafriri, Classical Banach spaces I. Function spaces, Springer-Yerlag, Berlin 1979.