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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-3-3,
author = {Antonis Manoussakis and Anna Pelczar-Barwacz},
title = {Types of tightness in spaces with unconditional basis},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {243-264},
zbl = {1314.46010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-3-3}
}
Antonis Manoussakis; Anna Pelczar-Barwacz. Types of tightness in spaces with unconditional basis. Studia Mathematica, Tome 223 (2014) pp. 243-264. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-3-3/