# Uniqueness of unconditional bases of ${c}_{0}\left({l}_{p}\right)$, 0 < p < 1

Studia Mathematica (1992)

- Volume: 102, Issue: 3, page 193-207
- ISSN: 0039-3223

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topLeránoz, C.. "Uniqueness of unconditional bases of $c_{0}(l_{p})$, 0 < p < 1." Studia Mathematica 102.3 (1992): 193-207. <http://eudml.org/doc/215922>.

@article{Leránoz1992,

abstract = {We prove that if 0 < p < 1 then a normalized unconditional basis of a complemented subspace of $c_0(l_p)$ must be equivalent to a permutation of a subset of the canonical unit vector basis of $c_0(l_p)$. In particular, $c_0(l_p)$ has unique unconditional basis up to permutation. Bourgain, Casazza, Lindenstrauss, and Tzafriri have previously proved the same result for $c_0(l₁)$.},

author = {Leránoz, C.},

journal = {Studia Mathematica},

keywords = {normalized unconditional basis; complemented subspace},

language = {eng},

number = {3},

pages = {193-207},

title = {Uniqueness of unconditional bases of $c_\{0\}(l_\{p\})$, 0 < p < 1},

url = {http://eudml.org/doc/215922},

volume = {102},

year = {1992},

}

TY - JOUR

AU - Leránoz, C.

TI - Uniqueness of unconditional bases of $c_{0}(l_{p})$, 0 < p < 1

JO - Studia Mathematica

PY - 1992

VL - 102

IS - 3

SP - 193

EP - 207

AB - We prove that if 0 < p < 1 then a normalized unconditional basis of a complemented subspace of $c_0(l_p)$ must be equivalent to a permutation of a subset of the canonical unit vector basis of $c_0(l_p)$. In particular, $c_0(l_p)$ has unique unconditional basis up to permutation. Bourgain, Casazza, Lindenstrauss, and Tzafriri have previously proved the same result for $c_0(l₁)$.

LA - eng

KW - normalized unconditional basis; complemented subspace

UR - http://eudml.org/doc/215922

ER -

## References

top- [1] A. Bonami, Ensembles Λ (p) dans le dual ${D}^{\infty}$, Ann. Inst. Fourier (Grenoble) 18 (2) (1968), 193-204.
- [2] J. Bourgain, P. G. Casazza, J. Lindenstrauss and L. Tzafriri, Banach spaces with a unique unconditional basis, up to permutation, Mem. Amer. Math. Soc. 322 (1985). Zbl0575.46011
- [3] N. J. Kalton, Orlicz sequence spaces without local convexity, Math. Proc. Cambridge Philos. Soc. 81 (1977), 253-278. Zbl0345.46013
- [4] N. J. Kalton, Banach envelopes of non-locally convex spaces, Canad. J. Math. 38 (1986), 65-86. Zbl0577.46016
- [5] N. J. Kalton, C. Leránoz and P. Wojtaszczyk, Uniqueness of unconditional bases in quasi-Banach spaces with applications to Hardy spaces, Israel J. Math. 72 (1990), 299-311. Zbl0753.46013
- [6] N. J. Kalton, N. T. Peck and J. W. Roberts, An F-space Sampler, London Math. Soc. Lecture Note Ser. 89, Cambridge University Press, 1985.
- [7] C. Leránoz, Uniqueness of unconditional bases in quasi-Banach spaces, Ph.D. thesis, University of Missouri-Columbia, 1990.
- [8] J. Lindenstrauss and A. Pełczyński, Absolutely summing operators in ${\mathcal{L}}_{p}$-spaces and their applications, Studia Math. 29 (1968), 275-326. Zbl0183.40501
- [9] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II. Function Spaces, Springer, Berlin 1979. Zbl0403.46022
- [10] J. Lindenstrauss and M. Zippin, Banach spaces with a unique unconditional basis, J. Funct. Anal. 3 (1969), 115-125. Zbl0174.17201
- [11] B. Maurey, Type et cotype dans les espaces munis de structures locales inconditionnelles, in: Sém. Maurey-Schwartz 1973-1974, Exposés 24-25, École Polytechnique, Paris.

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