Compact matrix operators on a new sequence space related to ℓ p $\ell_{p}$ spaces
Abstract In this paper, we derive some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on the sequence space ℓ p ( r , s , t ; B ( m ) ) $\ell_{p}(r,s,t;B^{(m)})$ which is related to ℓ p $\ell_{p}$ spaces. By applying the Hausdo...
Main Authors: | , , |
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Format: | Article |
Language: | English |
Published: |
SpringerOpen
2016-08-01
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Series: | Journal of Inequalities and Applications |
Subjects: | |
Online Access: | http://link.springer.com/article/10.1186/s13660-016-1129-6 |
Summary: | Abstract In this paper, we derive some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on the sequence space ℓ p ( r , s , t ; B ( m ) ) $\ell_{p}(r,s,t;B^{(m)})$ which is related to ℓ p $\ell_{p}$ spaces. By applying the Hausdorff measure of noncompactness, we obtain the necessary and sufficient conditions for such operators to be compact. Further, we study some geometric properties of this space. |
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ISSN: | 1029-242X |