Title :

Local Banach-space dichotomies and ergodic spaces

Author(s) :

Cuellar Carrera, Wilson [Auteur]
Universidade de São Paulo = University of São Paulo [USP]
De Rancourt, Noé [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]
Univerzita Karlova [Praha, Česká republika] = Charles University [Prague, Czech Republic] [UK]
Universität Wien = University of Vienna
Département de Mathématiques et Applications - ENS-PSL [DMA]
Ferenczi, Valentin [Auteur]
Universidade de São Paulo = University of São Paulo [USP]
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG (UMR_7586)]

Journal title :

Journal of the European Mathematical Society

Pages :

3537-3598

Publisher :

European Mathematical Society

Publication date :

2022-09-19

ISSN :

1435-9855

English keyword(s) :

Ergodic Banach spaces
Ramsey theory
Banach-space dichotomies
Non-Hilbertian spaces
Minimal Banach spaces
Hereditarily indecomposable Banach spaces

HAL domain(s) :

Mathématiques [math]/Analyse fonctionnelle [math.FA]
Mathématiques [math]/Combinatoire [math.CO]
Mathématiques [math]/Logique [math.LO]

English abstract : [en]

We prove a local version of Gowers' Ramsey-type theorem [25], as well as local versions both of the Banach space first dichotomy (the "unconditional/HI" dichotomy) of Gowers [25] and of the third dichotomy (the "minimal/tight" ...
Show more >We prove a local version of Gowers' Ramsey-type theorem [25], as well as local versions both of the Banach space first dichotomy (the "unconditional/HI" dichotomy) of Gowers [25] and of the third dichotomy (the "minimal/tight" dichotomy) due to Ferenczi-Rosendal [22]. This means that we obtain versions of these dichotomies restricted to certain families of subspaces called D-families, of which several concrete examples are given. As a main example, non-Hilbertian spaces form D-families; therefore versions of the above properties for non-Hilbertian spaces appear in new Banach space dichotomies. As a consequence we obtain new information on the number of subspaces of non-Hilbertian Banach spaces, making some progress towards the "ergodic" conjecture of Ferenczi-Rosendal and towards a question of Johnson.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL