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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 $c_{0} (l ₁)$ .

Uniqueness of unconditional basis of $ℓ_{p} (c ₀)$ and $ℓ_{p} (ℓ ₂)$ , 0 < p < 1

F. Albiac; C. Leránoz — 2002

Studia Mathematica

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.

The Tsirelson space $𝒯 (p)$ has a unique unconditional basis up to permutation for $0 < p < 1$ .

Albiac, F.; Leránoz, C. — 2009

Abstract and Applied Analysis

On perfectly homogeneous bases in quasi-Banach spaces.

Albiac, F.; Leránoz, C. — 2009

Abstract and Applied Analysis

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Currently displaying 1 – 4 of 4

Uniqueness of unconditional bases of c 0 ( l p ) , 0 < p < 1

Uniqueness of unconditional basis of ℓ p ( c ₀ ) and ℓ p ( ℓ ₂ ) , 0 < p < 1

The Tsirelson space 𝒯 ( p ) has a unique unconditional basis up to permutation for 0 < p < 1 .

On perfectly homogeneous bases in quasi-Banach spaces.

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

Uniqueness of unconditional basis of $ℓ_{p} (c ₀)$ and $ℓ_{p} (ℓ ₂)$ , 0 < p < 1

The Tsirelson space $𝒯 (p)$ has a unique unconditional basis up to permutation for $0 < p < 1$ .