Types of tightness in spaces with unconditional basis

Antonis Manoussakis, and Anna Pelczar-Barwacz. "Types of tightness in spaces with unconditional basis." Studia Mathematica 220.3 (2014): 243-264. <http://eudml.org/doc/285392>.

@article{AntonisManoussakis2014,
abstract = {We present a reflexive Banach space with an unconditional basis which is quasi-minimal and tight by range, i.e. of type (4) in Ferenczi-Rosendal's list related to Gowers' classification program of Banach spaces, but in contrast to the recently constructed space of type (4), our space is also tight with constants, thus essentially extending the list of known examples in Gowers' program. The space is defined on the basis of a boundedly modified mixed Tsirelson space with the use of a special coding function.},
author = {Antonis Manoussakis, Anna Pelczar-Barwacz},
journal = {Studia Mathematica},
keywords = {classification of Banach spaces; quasi-minimal Banach spaces; tight Banach spaces; mixed Tsirelson spaces; dichotomy},
language = {eng},
number = {3},
pages = {243-264},
title = {Types of tightness in spaces with unconditional basis},
url = {http://eudml.org/doc/285392},
volume = {220},
year = {2014},
}

TY - JOUR
AU - Antonis Manoussakis
AU - Anna Pelczar-Barwacz
TI - Types of tightness in spaces with unconditional basis
JO - Studia Mathematica
PY - 2014
VL - 220
IS - 3
SP - 243
EP - 264
AB - We present a reflexive Banach space with an unconditional basis which is quasi-minimal and tight by range, i.e. of type (4) in Ferenczi-Rosendal's list related to Gowers' classification program of Banach spaces, but in contrast to the recently constructed space of type (4), our space is also tight with constants, thus essentially extending the list of known examples in Gowers' program. The space is defined on the basis of a boundedly modified mixed Tsirelson space with the use of a special coding function.
LA - eng
KW - classification of Banach spaces; quasi-minimal Banach spaces; tight Banach spaces; mixed Tsirelson spaces; dichotomy
UR - http://eudml.org/doc/285392
ER -