Certain sequence spaces over the non-Newtonian complex field (Q2319055)

Summary: It is known from functional analysis that in classical calculus, the sets \(\omega\), \(\ell_{\infty}\), \(c\), \(c_0\) 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 \(0 < p < \infty\). In this study, our main goal is to construct the spaces \(\omega^{*}\), \(\ell_{\infty}^{*}\), \(c^{*}\), \(c_0^{*}\) and \(\ell_p^{*}\) over the non-Newtonian complex field \(\mathbb{C}^{*}\) and to obtain the corresponding results for these spaces, where \(\ddot{0} \ddot{<} p \ddot{<} \infty\).