Absolute cesàro series spaces and matrix operators

Abstract

In this paper we derive a series space | C? , µ| k using the well known absolute Cesàro summability | C? , µ| k of Das (Proc. Camb. Philol. Soc. 67:321–326, 1970), compute its ß-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). © 2017, Springer Science+Business Media B.V., part of Springer Nature.