On the properties of quasi-Banach function spaces

Fuente: arXiv
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Auteurs principaux: Nekvinda, Aleš, Peša, Dalimil
Format: Preprint
Publié: 2020
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author Nekvinda, Aleš
Peša, Dalimil
author_facet Nekvinda, Aleš
Peša, Dalimil
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2004_09435
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle On the properties of quasi-Banach function spaces
Nekvinda, Aleš
Peša, Dalimil
Functional Analysis
46A16, 46E30
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.
title On the properties of quasi-Banach function spaces
topic Functional Analysis
46A16, 46E30
url https://arxiv.org/abs/2004.09435