论文标题
关于准巴纳赫函数空间的属性
On the properties of quasi-Banach function spaces
论文作者
论文摘要
在本文中，我们探讨了在应用程序中很重要的准巴纳赫功能空间的一些基本属性。也就是说，我们表明它们具有Riesz的广义版本 - 菲舍尔属性，它们之间的嵌入始终是连续的，并且扩张操作员在它们上受到界定。我们还提供了在欧几里得空间上准巴纳赫功能空间的可分离性的表征。此外，我们将经典的riesz--fischer定理扩展到了准空间的背景，因此，获得了准 - 巴纳赫函数空间的替代性证明。
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.
