A study on absolute euler totient series space and certain matrix transformations

Abstract

Recently, many authors have focused on the studies related to sequence and series spaces. In the literature the simple andfundamental method is to construct new sequence and series spaces by means of the matrix domain of triangularmatrices on the classical sequence spaces. Based on this approach, in this study, we introduce a new series space ???? ?? asthe set of all series summable by absolute summability method ??, ???? ?? , where ?? = ?????? denotes Euler totient matrix,?? = ???? is a sequence of non-negative terms and ?? ? 1. Also, we show that the series space ???? ?? is linearly isomorphicto the space of all ??- absolutely summable sequences ??? for ?? ? 1. Moreover, we determine some topological propertiesand ??, ?? and ??-duals of this space and give Schauder basis for the space ???? ?? . Finally, we characterize the classes of thematrix operators from the space |???? |?? to the classical spaces ?? , ??, ??0, ?1 for 1 ? ?? < ? and vice versa.