Measures of Noncompactness and Condensing Operators:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1992
|
| Schriftenreihe: | Operator Theory: Advances and Applications
55 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | A condensing (or densifying) operator is a mapping under which the image of any set is in a certain sense more compact than the set itself. The degree of noncompactness of a set is measured by means of functions called measures of noncompactness. The contractive maps and the compact maps [i.e., in this Introduction, the maps that send any bounded set into a relatively compact one; in the main text the term "compact" will be reserved for the operators that, in addition to having this property, are continuous, i.e., in the authors' terminology, for the completely continuous operators] are condensing. For contractive maps one can take as measure of noncompactness the diameter of a set, while for compact maps can take the indicator function of a family of non-relatively com pact sets. The operators of the form F( x) = G( x, x), where G is contractive in the first argument and compact in the second, are also condensing with respect to some natural measures of noncompactness. The linear condensing operators are characterized by the fact that almost all of their spectrum is included in a disc of radius smaller than one. The examples given above show that condensing operators are a sufficiently typical phenomenon in various applications of functional analysis, for example, in the theory of differential and integral equations. As is turns out, the condensing operators have properties similar to the compact ones |
| Beschreibung: | 1 Online-Ressource (VIII, 252 p) |
| ISBN: | 9783034857277 9783034857291 |
| ISSN: | 0255-0156 |
| DOI: | 10.1007/978-3-0348-5727-7 |
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| 245 | 1 | 0 | |a Measures of Noncompactness and Condensing Operators |c by R. R. Akhmerov, M. I. Kamenskii, A. S. Potapov, A. E. Rodkina, B. N. Sadovskii |
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| 490 | 0 | |a Operator Theory: Advances and Applications |v 55 |x 0255-0156 | |
| 500 | |a A condensing (or densifying) operator is a mapping under which the image of any set is in a certain sense more compact than the set itself. The degree of noncompactness of a set is measured by means of functions called measures of noncompactness. The contractive maps and the compact maps [i.e., in this Introduction, the maps that send any bounded set into a relatively compact one; in the main text the term "compact" will be reserved for the operators that, in addition to having this property, are continuous, i.e., in the authors' terminology, for the completely continuous operators] are condensing. For contractive maps one can take as measure of noncompactness the diameter of a set, while for compact maps can take the indicator function of a family of non-relatively com pact sets. The operators of the form F( x) = G( x, x), where G is contractive in the first argument and compact in the second, are also condensing with respect to some natural measures of noncompactness. The linear condensing operators are characterized by the fact that almost all of their spectrum is included in a disc of radius smaller than one. The examples given above show that condensing operators are a sufficiently typical phenomenon in various applications of functional analysis, for example, in the theory of differential and integral equations. As is turns out, the condensing operators have properties similar to the compact ones | ||
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| 700 | 1 | |a Sadovskii, B. N. |e Sonstige |4 oth | |
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Datensatz im Suchindex
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| author | Akhmerov, R. R. |
| author_facet | Akhmerov, R. R. |
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| discipline | Allgemeine Naturwissenschaft Mathematik |
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| isbn | 9783034857277 9783034857291 |
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| spelling | Akhmerov, R. R. Verfasser aut Measures of Noncompactness and Condensing Operators by R. R. Akhmerov, M. I. Kamenskii, A. S. Potapov, A. E. Rodkina, B. N. Sadovskii Basel Birkhäuser Basel 1992 1 Online-Ressource (VIII, 252 p) txt rdacontent c rdamedia cr rdacarrier Operator Theory: Advances and Applications 55 0255-0156 A condensing (or densifying) operator is a mapping under which the image of any set is in a certain sense more compact than the set itself. The degree of noncompactness of a set is measured by means of functions called measures of noncompactness. The contractive maps and the compact maps [i.e., in this Introduction, the maps that send any bounded set into a relatively compact one; in the main text the term "compact" will be reserved for the operators that, in addition to having this property, are continuous, i.e., in the authors' terminology, for the completely continuous operators] are condensing. For contractive maps one can take as measure of noncompactness the diameter of a set, while for compact maps can take the indicator function of a family of non-relatively com pact sets. The operators of the form F( x) = G( x, x), where G is contractive in the first argument and compact in the second, are also condensing with respect to some natural measures of noncompactness. The linear condensing operators are characterized by the fact that almost all of their spectrum is included in a disc of radius smaller than one. The examples given above show that condensing operators are a sufficiently typical phenomenon in various applications of functional analysis, for example, in the theory of differential and integral equations. As is turns out, the condensing operators have properties similar to the compact ones Science (General) Science, general Naturwissenschaft Kondensierender Operator (DE-588)4295481-2 gnd rswk-swf Nichtkompaktheitsmaß (DE-588)4295482-4 gnd rswk-swf Kondensierender Operator (DE-588)4295481-2 s Nichtkompaktheitsmaß (DE-588)4295482-4 s 1\p DE-604 Kamenskii, M. I. Sonstige oth Potapov, A. S. Sonstige oth Rodkina, A. E. Sonstige oth Sadovskii, B. N. Sonstige oth https://doi.org/10.1007/978-3-0348-5727-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Akhmerov, R. R. Measures of Noncompactness and Condensing Operators Science (General) Science, general Naturwissenschaft Kondensierender Operator (DE-588)4295481-2 gnd Nichtkompaktheitsmaß (DE-588)4295482-4 gnd |
| subject_GND | (DE-588)4295481-2 (DE-588)4295482-4 |
| title | Measures of Noncompactness and Condensing Operators |
| title_auth | Measures of Noncompactness and Condensing Operators |
| title_exact_search | Measures of Noncompactness and Condensing Operators |
| title_full | Measures of Noncompactness and Condensing Operators by R. R. Akhmerov, M. I. Kamenskii, A. S. Potapov, A. E. Rodkina, B. N. Sadovskii |
| title_fullStr | Measures of Noncompactness and Condensing Operators by R. R. Akhmerov, M. I. Kamenskii, A. S. Potapov, A. E. Rodkina, B. N. Sadovskii |
| title_full_unstemmed | Measures of Noncompactness and Condensing Operators by R. R. Akhmerov, M. I. Kamenskii, A. S. Potapov, A. E. Rodkina, B. N. Sadovskii |
| title_short | Measures of Noncompactness and Condensing Operators |
| title_sort | measures of noncompactness and condensing operators |
| topic | Science (General) Science, general Naturwissenschaft Kondensierender Operator (DE-588)4295481-2 gnd Nichtkompaktheitsmaß (DE-588)4295482-4 gnd |
| topic_facet | Science (General) Science, general Naturwissenschaft Kondensierender Operator Nichtkompaktheitsmaß |
| url | https://doi.org/10.1007/978-3-0348-5727-7 |
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