Each operator in \({\mathfrak L}(l^p,l^r) (1\leq r<p<\infty)\) is compact (Q1128030)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Each operator in \({\mathfrak L}(l^p,l^r) (1\leq r |
scientific article; zbMATH DE number 1186792
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Each operator in \({\mathfrak L}(l^p,l^r) (1\leq r<p<\infty)\) is compact |
scientific article; zbMATH DE number 1186792 |
Statements
Each operator in \({\mathfrak L}(l^p,l^r) (1\leq r<p<\infty)\) is compact (English)
0 references
28 October 1998
0 references
Using construction of normalized block basis it can be proved that each bounded operator from \(\ell^p\) into \(\ell^r\), (\(1\leq r< p<\infty\)) is compact. This result can also be obtained using theory of norm ideals. The aim of this note is to present a very elementary proof of this important and useful fact.
0 references
norm ideals
0 references
0.86076176
0 references
0.85270876
0 references
0.8516396
0 references
0.85080725
0 references
