Banach Spaces of Type p have Arbitrarily Distortable Subspaces.
N. Tomczak-Jaegermann (1996)
Geometric and functional analysis
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N. Tomczak-Jaegermann (1996)
Geometric and functional analysis
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W.T. Gowers (1996)
Geometric and functional analysis
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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.
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.
G. Schechtman (1978-1979)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
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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...
I. Gasparis (2002)
Studia Mathematica
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A family is constructed of cardinality equal to the continuum, whose members are totally incomparable hereditarily indecomposable Banach spaces.
Gilles Pisier (1978)
Compositio Mathematica
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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.
Przemyslaw Wojtaszczyk (1972)
Mémoires de la Société Mathématique de France
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David Dean, Ivan Singer, Leonard Stembach (1971)
Studia Mathematica
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I. Edelstein, P. Wojtaszczyk (1976)
Studia Mathematica
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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...
Christian Rosendal (2011)
Studia Mathematica
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We give an intrinsic characterisation of the separable reflexive Banach spaces that embed into separable reflexive spaces with an unconditional basis all of whose normalised block sequences with the same growth rate are equivalent. This uses methods of E. Odell and T. Schlumprecht.
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...