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Applications of the Hausdorff Measure of Noncompactness on the Space \(l_p(r,s, t; B^{(m)})\), \(1\le p< \infty \)

  • Amit MajiEmail author
  • P. D. Srivastava
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 91)

Abstract

In this paper, we have introduced a sequence space \(l_p(r,s, t; B^{(m)})\), \(1\le p< \infty \) and proved that the space is a complete normed linear space. We have also shown that the space \(l_p(r,s, t; B^{(m)})\) is linearly isomorphic to \(l_p\) for \(1\le p< \infty \). Further, we have established some identities or estimates for the operator norms and the Hausdorff measure of noncompactness of certain matrix operators on this space. Finally, we have characterized some classes of compact operators on this space.

Keywords

Difference operator Sequence space Hausdorff measure of noncompactness Compact operators 

2010 Mathematics Subject Classification

46A45 46B15 46B50 40A05 

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Copyright information

© Springer India 2014

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology KharagpurKharagpurIndia

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