On the relation between several notions of unconditional structure - A counterexample
G. Schechtman (1978-1979)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
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G. Schechtman (1978-1979)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
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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.
D. R. Lewis (1975)
Compositio Mathematica
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Gilles Pisier (1978)
Compositio Mathematica
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J. Lindenstrauss (1980-1981)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
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L. Drewnowski (1987)
Colloquium Mathematicae
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James R. Holub (1998)
Annales Polonici Mathematici
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E. Tutaj has introduced classes of Schauder bases termed "unconditional-like" (UL) and "unconditional-like*" (UL*) whose intersection is the class of unconditional bases. In view of this association with unconditional bases, it is interesting to note that there exist Banach spaces which have no unconditional basis and yet have a basis of one of these two types (e.g., the space 𝓞[0,1]). In the same spirit, we show in this paper that the space of all compact operators on a reflexive Banach...
D. Alspach, P. Enflo, E. Odell (1977)
Studia Mathematica
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I. Edelstein, P. Wojtaszczyk (1976)
Studia Mathematica
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Albiac, F., Leránoz, C. (2009)
Abstract and Applied Analysis
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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.
Vladimir P. Fonf, Anatolij M. Plichko, V. V. Shevchik (2001)
RACSAM
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Sea T un operador lineal acotado e inyectivo de un espacio de Banach X en un espacio de Hilbert H con rango denso y sea {x} ⊂ X una sucesión tal que {Tx} es ortogonal. Se estudian propiedades de {Tx} dependientes de propiedades de {x}. También se estudia la ""situación opuesta"", es decir, la acción de un operador T : H → X sobre sucesiones ortogonales.
G. Schechtman (1978-1979)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
Similarity: