Almost convergence and Euler totient matrix

Abstract

This paper is devoted to study the almost convergent sequence space \(\widehat{c}(\varPhi )\) derived by the Euler totient matrix. It is proved that the space \(\widehat{c}(\varPhi )\) and the space of all almost convergent sequences are linearly isomorphic. Further, the \(\beta \)-dual of the space \(\widehat{c}(\varPhi )\) is determined and Euler totient core of a complex-valued sequence has been defined. Finally, inclusion theorems related to this new type of core are obtained.

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Correspondence to Emrah Evren Kara.

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Communicated by Yong Jiao.

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Demiriz, S., İlkhan, M. & Kara, E.E. Almost convergence and Euler totient matrix. Ann. Funct. Anal. 11, 604–616 (2020). https://doi.org/10.1007/s43034-019-00041-0

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Keywords

  • Euler function
  • Almost convergence
  • Euler totient matrix
  • Möbius function
  • Core theorems

Mathematics Subject Classification

  • 46A45
  • 40A05
  • 46A35