Displaying similar documents to “An Arithmetic Characterization of Decomposition Methods in Banach Spaces Similar to Pełczyński's Decomposition Method”

Cantor-Schroeder-Bernstein quadruples for Banach spaces

Elói Medina Galego (2008)

Colloquium Mathematicae

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Two Banach spaces X and Y are symmetrically complemented in each other if there exists a supplement of Y in X which is isomorphic to some supplement of X in Y. In 1996, W. T. Gowers solved the Schroeder-Bernstein (or Cantor-Bernstein) Problem for Banach spaces by constructing two non-isomorphic Banach spaces which are symmetrically complemented in each other. In this paper, we show how to modify such a symmetry in order to ensure that X is isomorphic to Y. To do this, first we introduce...

The Schroeder-Bernstein index for Banach spaces

Elói Medina Galego (2004)

Studia Mathematica

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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...

Duality, reflexivity and atomic decompositions in Banach spaces

Daniel Carando, Silvia Lassalle (2009)

Studia Mathematica

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We study atomic decompositions and their relationship with duality and reflexivity of Banach spaces. To this end, we extend the concepts of "shrinking" and "boundedly complete" Schauder basis to the atomic decomposition framework. This allows us to answer a basic duality question: when an atomic decomposition for a Banach space generates, by duality, an atomic decomposition for its dual space. We also characterize the reflexivity of a Banach space in terms of properties of its atomic...

An amalgamation of the Banach spaces associated with James and Schreier, Part I: Banach-space structure

Alistair Bird, Niels Jakob Laustsen (2010)

Banach Center Publications

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We create a new family of Banach spaces, the James-Schreier spaces, by amalgamating two important classical Banach spaces: James' quasi-reflexive Banach space on the one hand and Schreier's Banach space giving a counterexample to the Banach-Saks property on the other. We then investigate the properties of these James-Schreier spaces, paying particular attention to how key properties of their 'ancestors' (that is, the James space and the Schreier space) are expressed in them. Our main...