Absolute Cesàro Series Spaces and Matrix Operators

In this paper we derive a series space |Cλ,μ|k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\vert C_{\lambda,\mu} \vert _{k}$\end{document} using the well known absolute Cesàro summability |Cλ,μ|k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\vert C_{\lambda,\mu} \vert _{k}$\end{document} of Das (Proc. Camb. Philol. Soc. 67:321–326, 1970), compute its β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\beta$\end{document}-dual, give some algebraic and topological properties, and characterize some matrix operators defined on that space. So we generalize some results of Bosanquet (J. Lond. Math. Soc. 20:39–48, 1945), Flett (Proc. Lond. Math. Soc. 7:113–141, 1957), Mehdi (Proc. Lond. Math. Soc. (3)10:180–199, 1960), Mazhar (Tohoku Math. J. 23:433–451, 1971), Orhan and Sarıgöl (Rocky Mt. J. Math. 23(3):1091–1097, 1993) and Sarıgöl (Commun. Math. Appl. 7(1):11–22, 2016; Math. Comput. Model. 55:1763–1769, 2012).