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Conditionality constants of quasi-greedy bases in super-reflexive Banach spaces

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Albiac F., Ansorena J., Garrigós G., Hernández E., Raja M.

Studia Mathematica

2015

tom 227

nr 2

133-140

We show that in a super-reflexive Banach space, the conditionality constants $k_{N}(ℬ)$ of a quasi-greedy basis ℬ grow at most like $O((log N)^{1-ε})$ for some 0 < ε < 1. This extends results by the third-named author and Wojtaszczyk (2014), where this property was shown for quasi-greedy bases in $L_{p}$ for 1 < p < ∞. We also give an example of a quasi-greedy basis ℬ in a reflexive Banach space with $k_{N}(ℬ) ≈ log N$.

Ograniczanie wyników

1 Studia Mathematica

1 Albiac F.

1 Ansorena J.

1 Garrigós G.

1 Hernández E.

1 Raja M.

1 2015

Wyniki wyszukiwania

Conditionality constants of quasi-greedy bases in super-reflexive Banach spaces