On some geometric properties of sequence spaces of generalized arithmetic divisor sum function

Recently, some new sequence spaces $\ell _{p}(\mathfrak{A}^{\alpha })$ $(0< p<\infty )$ , $c_{0}(\mathfrak{A}^{\alpha })$ , $c(\mathfrak{A}^{\alpha })$ , and $\ell _{\infty }(\mathfrak{A}^{\alpha })$ have been studied by Yaying et al. (Forum Math., 2024, https://doi.org/10.1515/forum-2023-0138 ) as matrix domains of $\mathfrak{A}^{\alpha }=(a_{n,v}^{\alpha })$ , where $$ a_{\mathfrak{m},v}^{\alpha }=\left \{ \textstyle\begin{array}{c@{\quad}c@{\quad}c} \dfrac{v^{\alpha }}{\rho ^{(\alpha )}(\mathfrak{m})} & , & v\mid \mathfrak{m}, \\ 0 & , & v\nmid \mathfrak{m},\end{array}\displaystyle \right . $$ and $\rho ^{(\alpha )}(\mathfrak{m}):=$ sum of the $\alpha ^{\text{th}}$ power of the positive divisors of $\mathfrak{m}\in \mathbb{N}$ . They obtained their duals, matrix transformations and associated compact matrix operators for these matrix classes. This article deals with some geometric properties of these sequence spaces.