$l^{\infty}(X) - l^{p}(Y)$ Summability of Mapping Matrices

Abstract

For Banach spaces $X$ and $Y$, $\mathcal{F}_{C,\delta}(X,Y)$ is a large and meaningful extension of the family $L(X,Y)$ of linear operators. For classical Banach sequence spaces $l^{\infty}(X)$ and $l^{p}(Y)$ ($p \geq 1$) we find a characterization of the $l^{\infty}(X) − l^{p}(Y)$ transformation of matrices of mappings in $\mathcal{F}_{C,\delta}(X,Y)$.