# Uniqueness of unconditional bases in ${c}_{0}$-products

Studia Mathematica (1999)

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

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topCasazza, 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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