The Schroeder-Bernstein index for Banach spaces

• Autorzy: Elói Medina Galego
• Języki publikacji: EN

Abstrakty

EN

In relation to some Banach spaces recently constructed by W. T. Gowers and B. Maurey, we introduce the notion of Schroeder-Bernstein index SBi(X) for every Banach space X. This index is related to complemented subspaces of X which contain some complemented copy of X. Then we establish the existence of a Banach space E which is not isomorphic to Eⁿ for every n ∈ ℕ, n ≥ 2, but has a complemented subspace isomorphic to E². In particular, SBi(E) is uncountable. The construction of E follows the approach given in 1996 by W. T. Gowers to obtain the first solution to the Schroeder-Bernstein Problem for Banach spaces.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B03: Isomorphic theory (including renorming) of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 164
• Numer: 1
• Strony: 29-38

Daty

wydano

2004

Twórcy

autor

Elói Medina Galego

• Department of Mathematics, IME, University of São Paulo, São Paulo 05315-970 Brazil

Identyfikatory

DOI

10.4064/sm164-1-2