Displaying similar documents to “Cantor-Schroeder-Bernstein quadruples for Banach spaces”

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...

Schroeder-Bernstein Quintuples for Banach Spaces

Elói Medina Galego (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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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 ⎧ X X p ⊕ Y q , ⎨ ⎩ Y t X r ⊕ Y s . Such quintuples are called Schroeder-Bernstein quintuples for Banach spaces and they yield a unification of the known decomposition...

Polynomial inequalities in Banach spaces

Mirosław Baran (2015)

Banach Center Publications

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We point out relations between the injective complexification of a real Banach space and polynomial inequalities. In particular we prove a generalization of a classical Szegő inequality to the case of polynomial mappings between Banach spaces. As an application we observe a complex version of known Bernstein-Szegő type inequalities.