We introduce a notion of disjoint envelope functions to study asymptotic structures of Banach spaces. The main result gives a new characterization of asymptotic- spaces in terms of the -behavior of “disjoint-permissible” vectors of constant coefficients. Applying this result to Tirilman spaces we obtain a negative solution to a conjecture of Casazza and Shura. Further investigation of the disjoint envelopes leads to a finite-representability result in the spirit of the Maurey-Pisier theorem.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm164-3-6,
author = {B\"unyamin Sar\i },
title = {Envelope functions and asymptotic structures in Banach spaces},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {283-306},
zbl = {1075.46008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm164-3-6}
}
Bünyamin Sarı. Envelope functions and asymptotic structures in Banach spaces. Studia Mathematica, Tome 162 (2004) pp. 283-306. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm164-3-6/