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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