A new sequence space and norm of certain matrix operators on this space

Authors

  • Davoud Foroutannia Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
  • Hadi Roopaei Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
Abstract:

In the present paper, we introduce the sequence space [{l_p}(E,Delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left|  sum_{j in {E_n}} x_j - sum_{j in E_{n + 1}} x_jright| ^p < infty right},] where $E=(E_n)$ is a partition of finite subsets of the positive integers and $pge 1$. We investigate its topological properties and inclusion relations. Moreover, we consider the problem of finding  the norm of certain matrix operators from  $l_p$ into $ l_p(E,Delta)$, and apply our results to Copson and Hilbert matrices.

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Journal title

volume 03  issue 1

pages  1- 12

publication date 2016-02-01

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