ON STRONGLY CONDENSING OPERATORS AT INFINITY
The paper introduces the notion of an operator strongly condensing at infinity, which is a natural variation of the notion of a locally strongly condensing operator at a finite point (introduced by the author earlier). It turns out that if such an operator is asymptotically linear, then its asymptot...
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| Main Author: | |
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| Format: | Article |
| Language: | Russian |
| Published: |
Moscow State Technical University of Civil Aviation
2016-11-01
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| Series: | Научный вестник МГТУ ГА |
| Subjects: | |
| Online Access: | https://avia.mstuca.ru/jour/article/view/240 |
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| Summary: | The paper introduces the notion of an operator strongly condensing at infinity, which is a natural variation of the notion of a locally strongly condensing operator at a finite point (introduced by the author earlier). It turns out that if such an operator is asymptotically linear, then its asymptotic derivative is compact. In particular, this notion allows to build examples of operators that are neither compact, nor condensing, not even -bounded. Such operators form a linear space. Some applications of the notion to the theory of bifurcation points are discussed. |
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| ISSN: | 2079-0619 2542-0119 |