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arXiv · 2004.09435

On the properties of quasi-Banach function spaces

Aleš Nekvinda·Dalimil Peša
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Abstract

In this paper we explore some basic properties of quasi-Banach function spaces which are important in applications. Namely, we show that they posses a generalised version of Riesz--Fischer property, that embeddings between them are always continuous and that the dilation operator is bounded on them. We also provide a characterisation of separability for quasi-Banach function spaces over the Euclidean space. Furthermore, we extend the classical Riesz--Fischer theorem to the context of quasinormed spaces and, as a consequence, obtain an alternative proof of completeness of quasi-Banach function spaces.

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Aleš Nekvinda, Dalimil Peša. 2024-04-07. On the properties of quasi-Banach function spaces. https://doi.org/10.1007/s12220-024-01673-y

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