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Measure of Noncompactness of Linear Operators between Spaces of Sequences That Are (N,q) Summable or Bounded

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Abstract

In this paper we investigate linear operators between arbitrary BK spaces X and spaces Y of sequences that are \({\text{(}}\bar N,q)\) summable or bounded. We give necessary and sufficient conditions for infinite matrices A to map X into Y. Further, the Hausdorff measure of noncompactness is applied to give necessary and sufficient conditions for A to be a compact operator.

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Authors
  1. E. Malkowsky
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  2. V. Rakocevic
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Malkowsky, E., Rakocevic, V. Measure of Noncompactness of Linear Operators between Spaces of Sequences That Are (N,q) Summable or Bounded. Czechoslovak Mathematical Journal 51, 505–522 (2001). https://doi.org/10.1023/A:1013727821173

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  • DOI: https://doi.org/10.1023/A:1013727821173

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