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

F. AlbiacJ. L. AnsorenaG. GarrigósE. HernándezM. Raja — 2015

Studia Mathematica

We show that in a super-reflexive Banach space, the conditionality constants k N ( ) of a quasi-greedy basis ℬ grow at most like O ( ( l o g 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 ( ) l o g N .

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