Certain Sequence Spaces over the Non-Newtonian Complex Field

Abstract

It is known from functional analysis that in classical calculus, the sets $\omega$, ${\ell }_{\mathrm{\infty }}$, $c$, $c_{\mathrm{0}}$ and ${\ell }_p$ of all bounded, convergent, null and $p$-absolutely summable sequences are Banach spaces with their natural norms and they are complete according to the metric reduced from their norm, where . In this study, our main goal is to construct the spaces ${\omega }^{\mathrm{*}}$, ${\ell }_{\mathrm{\infty }}^{\mathrm{*}}$, $c^{\mathrm{*}}$, $c_{\mathrm{0}}^{\mathrm{*}}$ and ${\ell }_p^{\mathrm{*}}$ over the non-Newtonian complex field ${ℂ}^{\mathrm{*}}$ and to obtain the corresponding results for these spaces, where .