Some $B$-Difference Sequence Spaces Derived by Generalized Means and Compact Operators

A. Maji, A. Manna, P. D. Srivastava

This paper presents new sequence spaces $X(r, s, t, p ; B)$ for $X \in \{ l_\infty(p),$ $c(p), c_0(p), l(p)\}$ defined by using generalized means and difference operator. It is shown that these spaces are complete paranormed spaces and the spaces inebreak $X(r, s, t, p ; B)$ for $X \in \{ c(p), c_0(p), l(p)\}$ have Schauder basis. Furthermore, the $\alpha$-, $\beta$-, $\gamma$- duals of these sequence spaces are computed and also obtained necessary and sufficient conditions for some matrix transformations from $X(r, s, t, p ;B)$ to $X$. Finally, some classes of compact operators on the space $l_p(r, s, t ;B)$ are characterized by using the Hausdorff measure of noncompactness.