Schroeder-Bernstein quintuples for Banach spaces

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

Abstrakty

EN

Let X and Y be two Banach spaces, each 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 obtain necessary and sufficient conditions on the quintuples (p, q, r, s, t) in N for X to be isomorphic to Y whenever [...]. Such quintuples are called Schroeder-Bernstein quintuples for Banach spaces and they yield a unification of the known decomposition methods in Banach spaces involving finite sums of X and Y, similar to Pelczynski's decomposition method. Inspired by this result, we also introduce the notion of Schroeder-Bernstein sextuples for Banach spaces and pose a conjecture which would complete their characterization.

Słowa kluczowe

EN

Schroeder-Bernstein problem; square-cube problem

PL

zagadnienie Schroedera-Bernsteina

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2006
• Tom: Vol. 54, no 2
• Strony: 113--124
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Galego E. M.

• Eloi Medina Galego Department of Mathematics - IME University of Sao Paulo, Sao Paulo 05315-970,

Bibliografia

• [1] P. G. Casazza, The Schroeder-Bernstein property for Banach spaces, in: Contemp. Math. 85, Amer. Math. Soc., 1989, 61-77.
• [2] E. M. Galego, An arithmetic characterization of decomposition methods in Banach spaces similar to Pelczyński's decomposition method, Bull. Polish Acad. Sci. Math. 52 (2004), 273-282.
• [3] —, On pairs of Banach spaces which are isomorphic to complemented subspaces of each other, Colloq. Math. 101 (2004), 279-287.
• [4] W. T. Gowers, A solution to the Schroeder-Bernstein problem for Banach spaces, Bull. London Math. Soc. 28 (1996), 297-304.
• [5] W. T. Gowers and B. Maurey, Banach spaces with small spaces of operators, Math. Ann. 307 (1997), 543-568.
• [6] A. Zsák, On Banach spaces with small spaces of operators, in: Trends in Banach Spaces and Operator Theory (Memphis, TN, 2001), Contemp. Math. 321, Amer. Math. Soc., Providence, HI, 2003, 347-369.