Kara, Merve IlkhanAydin, Dilek2025-10-112025-10-1120252473-6988https://doi.org/10.3934/math.2025329https://hdl.handle.net/20.500.12684/21516With the aid of the Euler totient function phi and its summation function inverted perpendicular, a new matrix O(phi, inverted perpendicular) = (delta(phi, inverted perpendicular)nk), where delta(phi, inverted perpendicular)(nk) = {(-1)n-k inverted perpendicular(k)/ O-phi(n) , n - 1 <= k <= n, 0, otherwise is constructed to define the domains l(p)(O(phi, inverted perpendicular)), l(infinity)(O(phi, inverted perpendicular)), and l(1)(O(phi, inverted perpendicular)). After obtaining the norms on these domains, it is proved that these spaces are linearly isomorphic to classical ones. Also, their dual spaces are determined. Finally, characterizations of several matrix mappings are stated and proved.en10.3934/math.2025329info:eu-repo/semantics/openAccessarithmetic divisor sum functionmatrix domaindual spacematrix mappingArticle103720672222-s2.0-105002356458WOS:001458927300004Q1Q1