Spectral-free methods in the theory of hereditarily indecomposable Banach spaces - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Bulletin of the Belgian Mathematical Society - Simon Stevin Année : 2020

Spectral-free methods in the theory of hereditarily indecomposable Banach spaces

Résumé

We give new and simple proofs of some classical properties of hereditarily indecomposable Banach spaces, including the result by W. T. Gowers and B. Maurey that a hereditarily indecomposable Banach space cannot be isomorphic to a proper subspace of itself. These proofs do not make use of spectral theory and therefore, they work in real spaces as well as in complex spaces. We use our method to prove some new results. For example, we give a quantitative version of the latter result by Gowers and Maurey and deduce that Banach spaces that are isometric to all of their subspaces should have an unconditional basis with unconditional constant arbitrarily close to $1$. We also study the homotopy relation between into isomorphisms from hereditarily indecomposable spaces.
Fichier principal
Vignette du fichier
HI.pdf (287.07 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Licence : Copyright (Tous droits réservés)

Dates et versions

hal-04406804 , version 1 (19-01-2024)

Licence

Copyright (Tous droits réservés)

Identifiants

Citer

Noé de Rancourt. Spectral-free methods in the theory of hereditarily indecomposable Banach spaces. Bulletin of the Belgian Mathematical Society - Simon Stevin, 2020, 27 (5), pp.775-787. ⟨10.36045/j.bbms.200123⟩. ⟨hal-04406804⟩
5 Consultations
2 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More