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We prove that a biorthogonal wavelet basis yields an unconditional basis in all spaces $L^{p} (ℝ^{d})$ with 1 < p < ∞, provided the biorthogonal wavelet set functions satisfy weak decay conditions. The biorthogonal wavelet set is associated with an arbitrary dilation matrix in any dimension.

Unconditional decompositions and local unconditional structures in some subspaces of $L_{p}$ , 1≤p<2

Andrzej Borzyszkowski (1983)

Studia Mathematica

Unconditionally convergent series of compact operators

Charles W. Swartz (1989)

Commentationes Mathematicae Universitatis Carolinae

Une propriété du type $p$ -stable

G. Pisier (1973/1974)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

Unicité de certaines bases inconditionnelles

J. Bourgain (1980/1981)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

Uniformly convex norms in spaces with unconditional basis

T. Figiel (1974/1975)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

Uniformly convex norms on Banach lattices

T. Figiel (1980)

Studia Mathematica

Uniformly Gâteaux Differentiable Norms in Spaces with Unconditional Basis

Rychter, Jan (2000)

Serdica Mathematical Journal

*Supported in part by GAˇ CR 201-98-1449 and AV 101 9003. This paper is based on a part of the author’s MSc thesis written under the supervison of Professor V. Zizler.It is shown that a Banach space X admits an equivalent uniformly Gateaux differentiable norm if it has an unconditional basis and X* admits an equivalent norm which is uniformly rotund in every direction.

Uniqueness of (...) Bases and Isometries of Banach Spaces.

Y. Gordon, R. Loewy (1979)

Mathematische Annalen

Uniqueness of some unconditional bases II

J. Lindenstrauss (1980/1981)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

Uniqueness of unconditional bases in $c_{0}$ -products

P. Casazza, N. Kalton (1999)

Studia Mathematica

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 $p_{n} ￬ 1$ , $N_{n + 1} \geq 2 N_{n}$ and $(p_{n} - p_{n + 1}) l o g N_{n}$ remains bounded.

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

C. Leránoz (1992)

Studia Mathematica

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 $c_{0} (l ₁)$ .

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Un lemme de H. P. Rosenthal

Una caracterización de los operadores de Fredholm y semi-Fredholm.

Una nota sobre los espacios de Sobolev anisótropos vectoriales LΓp (E)*.

Unconditional and normalised bases

Unconditional bases and the Radon-Nikodym property

Unconditional biorthogonal wavelet bases in $L^{p} (ℝ^{d})$

Unconditional decompositions and local unconditional structures in some subspaces of $L_{p}$ , 1≤p<2

Unconditionally convergent series of compact operators

Une propriété du type $p$ -stable

Unicité de certaines bases inconditionnelles

Uniformly convex norms in spaces with unconditional basis

Uniformly convex norms on Banach lattices

Uniformly Gâteaux Differentiable Norms in Spaces with Unconditional Basis

Uniqueness of (...) Bases and Isometries of Banach Spaces.

Uniqueness of some unconditional bases II

Uniqueness of unconditional bases in $c_{0}$ -products

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

Universal approximations of certain functionals in Banach spaces

Universal series by trigonometric system in weighted $L_{μ}^{1}$ spaces.

Universal simultaneous approximations of the coefficient functionals

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