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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.

Weak bases in p -adic spaces

N. De Grande-De Kimpe, J. Kąkol, C. Perez-Garcia, W. H. Schikhof (2002)

Bollettino dell'Unione Matematica Italiana

We study polar locally convex spaces over a non-archimedean non-trivially valued complete field with a weak topological basis. We prove two completeness theorems and a Hahn-Banach type theorem for locally convex spaces with a weak Schauder basis.

λ -similar bases.

Gupta, Manjul, Kamthan, P.K. (1987)

International Journal of Mathematics and Mathematical Sciences

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