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Almost convergence and Euler totient matrix

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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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Authors and Affiliations

  1. Department of Mathematics, Tokat Gaziosmanpaşa University, 60240, Tokat, Turkey

    Serkan Demiriz

  2. Department of Mathematics, Düzce University, 81620, Düzce, Turkey

    Merve İlkhan & Emrah Evren Kara

Authors
  1. Serkan Demiriz
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  2. Merve İlkhan
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  3. Emrah Evren Kara
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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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  • DOI: https://doi.org/10.1007/s43034-019-00041-0

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