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

Abstract

We develop new Banach sequence spaces $e_0^{a,b}\left(p,q\right)$ and $e_c^{a,b}\left(p,q\right)$ derived by the domain of generalized $\left(p,q\right)$ -Euler matrix $E^{a,b}\left(p,q\right)$ 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 $\alpha$ , $\beta$ , and $\gamma$ -duals of the spaces $e_0^{a,b}\left(p,q\right)$ and $e_c^{a,b}\left(p,q\right)$ . Certain classes of matrix transformations are characterized from $e_0^{a,b}\left(p,q\right)$ and $e_c^{a,b}\left(p,q\right)$ to $\mathsf{Z}\in \left\{{\ell }_{\infty },c,c_0,{\ell }_1,{\ell }_k\right\}$ . We obtain essential conditions of compactness of operators from $e_0^{a,b}\left(p,q\right)$ and $e_c^{a,b}\left(p,q\right)$ to $\mathsf{Z}\in \left\{{\ell }_{\infty },c,c_0,{\ell }_1,bs,cs,c{s}_0\right\}$ . Finally, under a definite functional $\mathrm{\varrho }$ and a weighted sequence of positive reals $\delta$ , we define a new sequence space ${\left(e_0^{a,b}\left(p,q,\delta \right)\right)}_{\mathrm{\varrho }}$ . 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.