Some new Cesàro sequence spaces of order $α$ - Savaşcı, Medine Yeşilkayagil; Başar, Feyzi (Ukrains’kyi Matematychnyi Zhurnal, 2024)
UDC 517.98We introduce the spaces $\ell_∞(C_α),$ $f(C_α),$ and $f_0(C_α)$ of Cesàro bounded, Cesàro almost convergent, and Cesàro almost null sequences of order $α,$ respectively. Moreover, we establish some inclusion relations for these spaces and determine the $α$-, $β$- and $γ$-duals of the spaces $\ell_∞(C_α)$ and $f(C_α).$ Finally, we characterize the classes of matrix transformations from the space $f(C_α)$ to any sequence space $Y$ and from any sequence space $Y$ to the space $f(C_α).$