Uniqueness of unconditional basis of ${\ell }_p\left(c₀\right)$ and ${\ell }_p\left(\ell ₂\right)$, 0 < p < 1

F. Albiac, and C. Leránoz. "Uniqueness of unconditional basis of $ℓ_{p}(c₀)$ and $ℓ_{p}(ℓ₂)$, 0 < p < 1." Studia Mathematica 150.1 (2002): 35-52. <http://eudml.org/doc/285144>.

@article{F2002,
abstract = {We prove that the quasi-Banach spaces $ℓ_\{p\}(c₀)$ and $ℓ_\{p\}(ℓ₂)$ (0 < p < 1) have a unique unconditional basis up to permutation. Bourgain, Casazza, Lindenstrauss and Tzafriri have previously proved that the same is true for the respective Banach envelopes $ℓ₁(c₀)$ and ℓ₁(ℓ₂). They used duality techniques which are not available in the non-locally convex case.},
author = {F. Albiac, C. Leránoz},
journal = {Studia Mathematica},
keywords = {quasi-Banach space; unconditional basis; unique unconditional basis up to permutation; Banach envelope},
language = {eng},
number = {1},
pages = {35-52},
title = {Uniqueness of unconditional basis of $ℓ_\{p\}(c₀)$ and $ℓ_\{p\}(ℓ₂)$, 0 < p < 1},
url = {http://eudml.org/doc/285144},
volume = {150},
year = {2002},
}

TY - JOUR
AU - F. Albiac
AU - C. Leránoz
TI - Uniqueness of unconditional basis of $ℓ_{p}(c₀)$ and $ℓ_{p}(ℓ₂)$, 0 < p < 1
JO - Studia Mathematica
PY - 2002
VL - 150
IS - 1
SP - 35
EP - 52
AB - We prove that the quasi-Banach spaces $ℓ_{p}(c₀)$ and $ℓ_{p}(ℓ₂)$ (0 < p < 1) have a unique unconditional basis up to permutation. Bourgain, Casazza, Lindenstrauss and Tzafriri have previously proved that the same is true for the respective Banach envelopes $ℓ₁(c₀)$ and ℓ₁(ℓ₂). They used duality techniques which are not available in the non-locally convex case.
LA - eng
KW - quasi-Banach space; unconditional basis; unique unconditional basis up to permutation; Banach envelope
UR - http://eudml.org/doc/285144
ER -