Envelope functions and asymptotic structures in Banach spaces

Bünyamin Sarı. "Envelope functions and asymptotic structures in Banach spaces." Studia Mathematica 164.3 (2004): 283-306. <http://eudml.org/doc/285087>.

@article{BünyaminSarı2004,
abstract = {We introduce a notion of disjoint envelope functions to study asymptotic structures of Banach spaces. The main result gives a new characterization of asymptotic-$ℓ_\{p\}$ spaces in terms of the $ℓ_\{p\}$-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.},
author = {Bünyamin Sarı},
journal = {Studia Mathematica},
keywords = {asymptotic structure; asymptotic space; disjoint envelope function; Tsirelson space},
language = {eng},
number = {3},
pages = {283-306},
title = {Envelope functions and asymptotic structures in Banach spaces},
url = {http://eudml.org/doc/285087},
volume = {164},
year = {2004},
}

TY - JOUR
AU - Bünyamin Sarı
TI - Envelope functions and asymptotic structures in Banach spaces
JO - Studia Mathematica
PY - 2004
VL - 164
IS - 3
SP - 283
EP - 306
AB - We introduce a notion of disjoint envelope functions to study asymptotic structures of Banach spaces. The main result gives a new characterization of asymptotic-$ℓ_{p}$ spaces in terms of the $ℓ_{p}$-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.
LA - eng
KW - asymptotic structure; asymptotic space; disjoint envelope function; Tsirelson space
UR - http://eudml.org/doc/285087
ER -