Some new paranormed sequence spaces and core theorems

摘要

Let μ ∈ {?_∞, c, c_0}. In this study, by using lambda matrix Λ and difference matrix B, we introduce the new nonabsolute type paranormed sequence space μ(λ,B; p) and prove that μ(λ,B; p) and μ(p) linearly isomorphic. Further, we give some inclusion relations concerning the space μ(λ,B; p). Afterwards, we determine the alpha-, beta- and gamma-duals of the space μ(λ, p;B). We also give the characterization of the classes (μ(λ,B; p):ν) and (ν:μ(λ,B; p)), where ν is any given sequence space. Moreover, we introduce the Λ-core of a complex valued sequence and determine the necessary and sufficient conditions on a matrix A for which Λ-core(Ax) ?K -core(x) and Λ-core(Ax) ? st -core(x) for all x ∈ ?_∞.