ON OPERATORS WITH THE SPHERICAL PROPERTY
Properties of continuous positively homogeneous operators of degree via various functions (e.g. measures of noncompactness) on all bounded subsets of a Banach space are studied. Necessary and sufficient conditions for these functions to vanish on the image of the unit ball under positively homogeneo...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | Russian |
| Published: |
Moscow State Technical University of Civil Aviation
2016-12-01
|
| Series: | Научный вестник МГТУ ГА |
| Subjects: | |
| Online Access: | https://avia.mstuca.ru/jour/article/view/857 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Properties of continuous positively homogeneous operators of degree via various functions (e.g. measures of noncompactness) on all bounded subsets of a Banach space are studied. Necessary and sufficient conditions for these functions to vanish on the image of the unit ball under positively homogeneous operators are given. In particular, we give criteria for the complete continuity of the Fréchet derivative in an arbitrary Banach space and criteria for operators, acting in regular spaces, to be improving. |
|---|---|
| ISSN: | 2079-0619 2542-0119 |