Measure of Noncompactness for Compact Matrix Operators on Some BK Spaces
We study the spaces w0p, wp, and w∞p of sequences that are strongly summable to 0, summable, and bounded with index p≥1 by the Cesàro method of order 1 and establish the representations of the general bounded linear operators from the spaces wp into the spaces w∞1, w1, and w01. We also give estimate...
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Hindawi Limited
2014-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2014/196489 |
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doaj-f3bf6e724e224291955dcbdb10073eb42020-11-24T23:49:56ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882014-01-01201410.1155/2014/196489196489Measure of Noncompactness for Compact Matrix Operators on Some BK SpacesE. Malkowsky0A. Alotaibi1Department of Mathematics, University of Giessen, Arndtstraβe 2, 35392 Giessen, GermanyDepartment of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi ArabiaWe study the spaces w0p, wp, and w∞p of sequences that are strongly summable to 0, summable, and bounded with index p≥1 by the Cesàro method of order 1 and establish the representations of the general bounded linear operators from the spaces wp into the spaces w∞1, w1, and w01. We also give estimates for the operator norm and the Hausdorff measure of noncompactness of such operators. Finally we apply our results to characterize the classes of compact bounded linear operators from w0p and wp into w01 and w1.http://dx.doi.org/10.1155/2014/196489 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
E. Malkowsky A. Alotaibi |
| spellingShingle |
E. Malkowsky A. Alotaibi Measure of Noncompactness for Compact Matrix Operators on Some BK Spaces Journal of Function Spaces |
| author_facet |
E. Malkowsky A. Alotaibi |
| author_sort |
E. Malkowsky |
| title |
Measure of Noncompactness for Compact Matrix Operators on Some BK Spaces |
| title_short |
Measure of Noncompactness for Compact Matrix Operators on Some BK Spaces |
| title_full |
Measure of Noncompactness for Compact Matrix Operators on Some BK Spaces |
| title_fullStr |
Measure of Noncompactness for Compact Matrix Operators on Some BK Spaces |
| title_full_unstemmed |
Measure of Noncompactness for Compact Matrix Operators on Some BK Spaces |
| title_sort |
measure of noncompactness for compact matrix operators on some bk spaces |
| publisher |
Hindawi Limited |
| series |
Journal of Function Spaces |
| issn |
2314-8896 2314-8888 |
| publishDate |
2014-01-01 |
| description |
We study the spaces w0p, wp, and w∞p of sequences that are strongly summable to 0, summable, and bounded with index p≥1 by the Cesàro method of order 1 and establish the representations of the general bounded linear operators from the spaces wp into the spaces w∞1, w1, and w01. We also give estimates for the operator norm and the Hausdorff measure of noncompactness of such operators. Finally we apply our results to characterize the classes of compact bounded linear operators from w0p and wp into w01 and w1. |
| url |
http://dx.doi.org/10.1155/2014/196489 |
| work_keys_str_mv |
AT emalkowsky measureofnoncompactnessforcompactmatrixoperatorsonsomebkspaces AT aalotaibi measureofnoncompactnessforcompactmatrixoperatorsonsomebkspaces |
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