Some Algebraic and Topological Properties of New Lucas Difference Sequence Spaces

Abstract

Karakas¸ and Karabudak [22], introduced the Lucas sequence spaces X(E) and studied their someproperties. The main purpose of this study is to introduce the Lucas difference sequence spaces c0(Lˆ, ∆) and c(Lˆ, ∆)by using the Lucas sequence. Also, we prove that the spaces c0(Lˆ, ∆) and c(Lˆ, ∆), are linearly isomorphic to spacesc0 and c, respectively. Besides this, the α−, β− and γ−duals of this spaces have been computed, their bases havebeen constructed and some topological properties of these spaces have been studied. Finally, the classes of matrices(c0(Lˆ, ∆) : µ) and (c(Lˆ, ∆) : µ) have been characterized, where µ is one of the sequence spaces `∞, c and c0 andderives the other characterizations for the special cases of µ.