Geodesic
A Banach space dichotomy theorem for quotients of subspaces
Valentin Ferenczi1
1 Institut de Mathématiques de Jussieu Projet Analyse Fonctionnelle Université Pierre et Marie Curie – Paris 6 Boîte 186, 4, Place Jussieu 75252 Paris Cedex 05, France
Studia Mathematica, Tome 180 (2007) no. 2, pp. 111-131

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

A Banach space $X$ with a Schauder basis is defined to have the restricted quotient hereditarily indecomposable property if $X/Y$ is hereditarily indecomposable for any infinite-codimensional subspace $Y$ with a successive finite-dimensional decomposition on the basis of $X$. The following dichotomy theorem is proved: any infinite-dimensional Banach space contains a quotient of a subspace which either has an unconditional basis, or has the restricted quotient hereditarily indecomposable property.
DOI : 10.4064/sm180-2-2
Keywords: banach space schauder basis defined have restricted quotient hereditarily indecomposable property hereditarily indecomposable infinite codimensional subspace successive finite dimensional decomposition basis following dichotomy theorem proved infinite dimensional banach space contains quotient subspace which either has unconditional basis has restricted quotient hereditarily indecomposable property

Valentin Ferenczi 1

1 Institut de Mathématiques de Jussieu Projet Analyse Fonctionnelle Université Pierre et Marie Curie – Paris 6 Boîte 186, 4, Place Jussieu 75252 Paris Cedex 05, France 
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Valentin Ferenczi. A Banach space dichotomy theorem for
 quotients of subspaces. Studia Mathematica, Tome 180 (2007) no. 2, pp. 111-131. doi: 10.4064/sm180-2-2

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