A Banach space dichotomy theorem for quotients of subspaces

• Autorzy: Valentin Ferenczi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 03E15: Descriptive set theory
• 46B03: Isomorphic theory (including renorming) of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 180
• Numer: 2
• Strony: 111-131

Daty

wydano

2007

Twórcy

autor

Valentin Ferenczi

• 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

Identyfikatory

DOI

10.4064/sm180-2-2