Korean J. Math.  Vol 28, No 2 (2020)  pp.361-378
DOI: https://doi.org/10.11568/kjm.2020.28.2.361

Domain of Euler-totient matrix operator in the space $\mathcal{L}_{p}$

Serkan Demiriz, Sezer Erdem

Abstract


The most apparent aspect of the present study is to introduce a new sequence space $\Phi^\star(\mathcal{L}_{p})$ derived by double Euler-Totient matrix operator. We examine its topological and algebraic properties and give an inclusion relation. In addition to those, the $\alpha-$, $\beta(bp)-$ and $\gamma-$duals of the space $\Phi^\star(\mathcal{L}_{p})$ are determined and finally, some 4-dimensional matrix mapping classes related to this space are characterized.


Keywords


Euler function, Möbius function, double Euler-Totient matrix, double sequence space, $\alpha$-, $\beta(bp)$- and $\gamma$-duals, matrix domain of 4-dimensional matrices, matrix transformations

Subject classification

46A06, 47B38

Sponsor(s)



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