Displaying similar documents to “A Banach space dichotomy theorem for quotients of subspaces”

Quotients with a shrinking basis

Jorge Mujica (2012)

Studia Mathematica

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We present a simple proof of a theorem that yields as a corollary a result of Valdivia that sharpens an old result of Johnson and Rosenthal.

On the structure of Banach spaces with an unconditional basic sequence

Razvan Anisca (2007)

Studia Mathematica

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For a Banach space X with an unconditional basic sequence, one of the following regular-irregular alternatives holds: either X contains a subspace isomorphic to ℓ₂, or X contains a subspace which has an unconditional finite-dimensional decomposition, but does not admit such a decomposition with a uniform bound for the dimensions of the decomposition. This result can be viewed in the context of Gowers' dichotomy theorem.

Incomparable, non-isomorphic and minimal Banach spaces

Christian Rosendal (2004)

Fundamenta Mathematicae

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A Banach space contains either a minimal subspace or a continuum of incomparable subspaces. General structure results for analytic equivalence relations are applied in the context of Banach spaces to show that if E₀ does not reduce to isomorphism of the subspaces of a space, in particular, if the subspaces of the space admit a classification up to isomorphism by real numbers, then any subspace with an unconditional basis is isomorphic to its square and hyperplanes, and the unconditional...

Decomposable subspaces of Banach spaces.

Manuel González, Antonio Martinón (2003)

RACSAM

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We introduce and study the notion of hereditarily A-indecomposable Banach space for A a space ideal. For a hereditarily A-indecomposable space X we show that the operators from X into a Banach space Y can be written as the union of two sets A Φ(X,Y) and A(X;Y ). For some ideals A defined in terms of incomparability, the first set is open, the second set correspond to a closed operator ideal and the union is disjoint.

A space C(K) where all nontrivial complemented subspaces have big densities

Piotr Koszmider (2005)

Studia Mathematica

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Using the method of forcing we prove that consistently there is a Banach space (of continuous functions on a totally disconnected compact Hausdorff space) of density κ bigger than the continuum where all operators are multiplications by a continuous function plus a weakly compact operator and which has no infinite-dimensional complemented subspaces of density continuum or smaller. In particular no separable infinite-dimensional subspace has a complemented superspace of density continuum...

Quotients of indecomposable Banach spaces of continuous functions

Rogério Augusto dos Santos Fajardo (2012)

Studia Mathematica

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Assuming ⋄, we construct a connected compact topological space K such that for every closed L ⊂ K the Banach space C(L) has few operators, in the sense that every operator on C(L) is multiplication by a continuous function plus a weakly compact operator. In particular, C(K) is indecomposable and has continuum many non-isomorphic indecomposable quotients, and K does not contain a homeomorphic copy of βℕ. Moreover, assuming CH we construct a connected compact K where...