Lorentz spaces and embeddings induced by almost greedy bases in superreflexive Banach spaces

2021/05/19 by Ansorena, José L., Bello, Glenier, Wojtaszczyk, Przemysław
#41A65 #46A25 #46A35 #46B10 #46B15 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2105.09203

Abstract

The aim of this paper is to show that almost greedy bases induce tighter embeddings in superreflexive Banach spaces than in general Banach spaces. More specifically, we show that an almost greedy basis in a superreflexive Banach space \mathbbX induces embeddings that allow squeezing \mathbbX between two superreflexive Lorentz sequence spaces that are close to each other in the sense that they have the same fundamental function.

Related

• Building highly conditional almost greedy and quasi-greedy bases in\n Banach spaces
• Building highly conditional quasi-greedy bases in classical Banach\n spaces
• Approximation spaces, greedy classes and Lorentz spaces
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• Conditional quasi-greedy bases in non-superreflexive Banach spaces