Uniqueness of unconditional bases in c 0 -products

P. Casazza; N. Kalton

Studia Mathematica (1999)

  • Volume: 133, Issue: 3, page 275-294
  • ISSN: 0039-3223

Abstract

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We give counterexamples to a conjecture of Bourgain, Casazza, Lindenstrauss and Tzafriri that if X has a unique unconditional basis (up to permutation) then so does c 0 ( X ) . We also give some positive results including a simpler proof that c 0 ( ℓ 1 ) has a unique unconditional basis and a proof that c 0 ( ℓ p n N n ) has a unique unconditional basis when p n ￬ 1 , N n + 1 ≥ 2 N n and ( p n - p n + 1 ) l o g N n remains bounded.

How to cite

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Casazza, P., and Kalton, N.. "Uniqueness of unconditional bases in $c_0$-products." Studia Mathematica 133.3 (1999): 275-294. <http://eudml.org/doc/216619>.

@article{Casazza1999,
abstract = {We give counterexamples to a conjecture of Bourgain, Casazza, Lindenstrauss and Tzafriri that if X has a unique unconditional basis (up to permutation) then so does $c_0(X)$. We also give some positive results including a simpler proof that $c_0(ℓ_1)$ has a unique unconditional basis and a proof that $c_0(ℓ_\{p_n\}^\{N_n\})$ has a unique unconditional basis when $p_n ￬ 1$, $N_\{n+1\} ≥ 2N_\{n\}$ and $(p_n-p_\{n+1\}) logN_\{n\}$ remains bounded.},
author = {Casazza, P., Kalton, N.},
journal = {Studia Mathematica},
keywords = {space ; unconditional basis; Tsirelson space},
language = {eng},
number = {3},
pages = {275-294},
title = {Uniqueness of unconditional bases in $c_0$-products},
url = {http://eudml.org/doc/216619},
volume = {133},
year = {1999},
}

TY - JOUR
AU - Casazza, P.
AU - Kalton, N.
TI - Uniqueness of unconditional bases in $c_0$-products
JO - Studia Mathematica
PY - 1999
VL - 133
IS - 3
SP - 275
EP - 294
AB - We give counterexamples to a conjecture of Bourgain, Casazza, Lindenstrauss and Tzafriri that if X has a unique unconditional basis (up to permutation) then so does $c_0(X)$. We also give some positive results including a simpler proof that $c_0(ℓ_1)$ has a unique unconditional basis and a proof that $c_0(ℓ_{p_n}^{N_n})$ has a unique unconditional basis when $p_n ￬ 1$, $N_{n+1} ≥ 2N_{n}$ and $(p_n-p_{n+1}) logN_{n}$ remains bounded.
LA - eng
KW - space ; unconditional basis; Tsirelson space
UR - http://eudml.org/doc/216619
ER -

References

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