Generalizations of Pelczynski`s decomposition method for Banach spaces containing a complemented copy of their squares
Contribuinte(s) |
UNIVERSIDADE DE SÃO PAULO |
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Data(s) |
20/10/2012
20/10/2012
2008
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Resumo |
Suppose that X and Y are Banach spaces isomorphic to complemented subspaces of each other. In 1996, W. T. Gowers solved the Schroeder- Bernstein Problem for Banach spaces by showing that X is not necessarily isomorphic to Y. However, if X-2 is complemented in X with supplement A and Y-2 is complemented in Y with supplement B, that is, { X similar to X-2 circle plus A Y similar to Y-2 circle plus B, then the classical Pelczynski`s decomposition method for Banach spaces shows that X is isomorphic to Y whenever we can assume that A = B = {0}. But unfortunately, this is not always possible. In this paper, we show that it is possible to find all finite relations of isomorphism between A and B which guarantee that X is isomorphic to Y. In order to do this, we say that a quadruple (p, q, r, s) in N is a P-Quadruple for Banach spaces if X is isomorphic to Y whenever the supplements A and B satisfy A(p) circle plus B-q similar to A(r) circle plus B-s . Then we prove that (p, q, r, s) is a P-Quadruple for Banach spaces if and only if p - r = s - q = +/- 1. |
Identificador |
ARCHIV DER MATHEMATIK, v.90, n.6, p.530-536, 2008 0003-889X http://producao.usp.br/handle/BDPI/30641 10.1007/s00013-008-2568-1 |
Idioma(s) |
eng |
Publicador |
BIRKHAUSER VERLAG AG |
Relação |
Archiv der Mathematik |
Direitos |
restrictedAccess Copyright BIRKHAUSER VERLAG AG |
Palavras-Chave | #Pelczynski`s decomposition method #Schroeder-Bernstein problem #SCHROEDER-BERNSTEIN PROBLEM #Mathematics |
Tipo |
article original article publishedVersion |