A STUDY ON ABSOLUTE EULER TOTIENT SERIES SPACE AND CERTAIN MATRIX TRANSFORMATIONS

Recently, many authors have focused on the studies related to sequence and series spaces. In the literature the simple and fundamental method is to construct new sequence and series spaces by means of the matrix domain of triangular matrices on the classical sequence spaces. Based on this approach, in this study, we introduce a new series space |ϕ_z |_p as the set of all series summable by absolute summability method |Φ,z_n |_p, where Φ=(ϕ_nk ) denotes Euler totient matrix, z=(z_n ) is a sequence of non-negative terms and p≥1. Also, we show that the series space |ϕ_z |_p is linearly isomorphic to the space of all p- absolutely summable sequences l_p for p≥1. Moreover, we determine some topological properties and α, β and γ-duals of this space and give Schauder basis for the space |ϕ_z |_p. Finally, we characterize the classes of the matrix operators from the space |ϕ_z |_p to the classical spaces l_∞,c,c_0,l_1 for 1≤p<∞ and vice versa.