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

100%

Leránoz C.

Studia Mathematica

1992

tom 102

nr 3

193-207

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 $c_0(l₁)$.

Uniqueness of unconditional basis of $ℓ_{p}(c₀)$ and $ℓ_{p}(ℓ₂)$, 0 < p < 1

63%

Albiac F., Leránoz C.

Studia Mathematica

2002

tom 150

nr 1

35-52

We prove that the quasi-Banach spaces $ℓ_{p}(c₀)$ and $ℓ_{p}(ℓ₂)$ (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 $ℓ₁(c₀)$ and ℓ₁(ℓ₂). They used duality techniques which are not available in the non-locally convex case.

Ograniczanie wyników

2 Studia Mathematica

2 Leránoz C.

1 Albiac F.

1 2002

1 1992

Wyniki wyszukiwania

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

Uniqueness of unconditional basis of $ℓ_{p}(c₀)$ and $ℓ_{p}(ℓ₂)$, 0 < p < 1