Some new Cesàro sequence spaces of order $\alpha$

Medine Yeşilkayagil Savaşcı; Feyzi Başar

doi:10.3842/umzh.v76i3.7333

Medine Yeşilkayagil Savaşcı Faculty of Applied Sciences, Uşak University, Turkey
Feyzi Başar Department of Primary Mathematics Teacher Education, İnönü University, Malatya, Turkey

DOI: https://doi.org/10.3842/umzh.v76i3.7333

Keywords: Normed sequence space, $\alpha$-, $\beta$- and $\gamma$-duals and matrix mappings

Abstract

UDC 517.98

We introduce the spaces $\ell_\infty(C_\alpha),$ $f(C_\alpha),$ and $f_0(C_\alpha)$ of Ces\`{a}ro bounded, Ces\`{a}ro almost convergent, and Ces\`{a}ro almost null sequences of order $\alpha,$ respectively. Moreover, we establish some inclusion relations for these spaces and determine the $\alpha$-, $\beta$- and $\gamma$-duals of the spaces $\ell_\infty(C_\alpha)$ and $f(C_\alpha).$ Finally, we characterize the classes of matrix transformations from the space $f(C_\alpha)$ to any sequence space $Y$ and from any sequence space $Y$ to the space $f(C_\alpha).$

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