Relations between approximation numbers and entropy numbers
Replacing in the definition of the norm the triangle inequality by the inequality \(\| u+v\|\leq c(\| u\|+ \| v\|)\), \(c\geq 1\) fixed, one obtains the notion of quasi-norm and the corresponding notion of quasi-Banach space. The aim of this paper is to study the interrelations between approximation numbers and entropy numbers of compact operators acting on quasi-Banach spaces. In the case of Banach spaces, similar results were obtained by B. Carl [see, e.g., \textit{B. Carl} and \textit{I. Stephani}, `Entropy compactness and the approximation of operators', Cambridge (1990; Zbl 0705.47017)]. Applications of general results to embedding operators between Besov-Hardy-Sobolev spaces are given.
compact operators acting on quasi-Banach spaces
scientific article; zbMATH DE number 636061