Uniqueness of unconditional basis of $ℓ_{p}(c₀)$ and $ℓ_{p}(ℓ₂)$, 0 < p < 1

F. Albiac; C. Leránoz

Uniqueness of unconditional basis of

ℓ_{p} (c ₀)

and

ℓ_{p} (ℓ ₂)

, 0 < p < 1

F. Albiac ; C. Leránoz

Studia Mathematica, Tome 151 (2002), p. 35-52 / Harvested from The Polish Digital Mathematics Library

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Résumé

We prove that the quasi-Banach spaces $ℓ_{p} (c ₀)$ and $ℓ_{p} (ℓ ₂)$ (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 $ℓ ₁ (c ₀)$ and ℓ₁(ℓ₂). They used duality techniques which are not available in the non-locally convex case.

Publié le : 2002-01-01

Zbl 1031.46006

EUDML-ID : urn:eudml:doc:285144

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     title = {Uniqueness of unconditional basis of $l\_{p}(c0)$ and $l\_{p}(l2)$, 0 < p < 1},
     journal = {Studia Mathematica},
     volume = {151},
     year = {2002},
     pages = {35-52},
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F. Albiac; C. Leránoz. Uniqueness of unconditional basis of $ℓ_{p}(c₀)$ and $ℓ_{p}(ℓ₂)$, 0 < p < 1. Studia Mathematica, Tome 151 (2002) pp. 35-52. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm150-1-4/