Superposition operators on some new type of order modular spaces

Abstract

Let E be a Riesz space and $\rho _{f}$
be an order modular where $f$ is an order $\varphi $-function. In this
paper, we introduce E-valued sequence spaces, namely $X(E,\rho _{f})$.
Further, we denote E-valued sequence spaces $c_{o}(E)$ and $\ell _{1}(E)$
of all $\sigma $-order convergent E-sequences and finite absolutely $%
\sigma $-order convergent E-series, respectively. We characterize the
classes $X(E,\rho _{f})$ into $\ell _{1}(E,\rho _{h})$ by superposition for $%
X\in \big\{c_{o},\ell _{1}\big\}$.