Mappings Ideal of Type the Domain of Generalized p , q -Euler Matrix in c 0 and c

Abstract

We develop new Banach sequence spaces e 0 a , b p , q and e c a , b p , q derived by the domain of generalized p , q -Euler matrix E a , b p , q in the spaces of null and convergent sequences, respectively. We investigate some topological properties and inclusion natures related to these spaces. We construct bases and obtain α , β , and γ -duals of the spaces e 0 a , b p , q and e c a , b p , q . Certain classes of matrix transformations are characterized from e 0 a , b p , q and e c a , b p , q to Z ∈ ℓ ∞ , c , c 0 , ℓ 1 , ℓ k . We obtain essential conditions of compactness of operators from e 0 a , b p , q and e c a , b p , q to Z ∈ ℓ ∞ , c , c 0 , ℓ 1 , b s , c s , c s 0 . Finally, under a definite functional ϱ and a weighted sequence of positive reals δ , we define a new sequence space e 0 a , b p , q , δ ϱ . Certain geometric and topological properties of this space along with the eigenvalue distribution of mapping ideals due to this space and s -numbers are investigated.