Geodesic
Some $B$-Difference Sequence Spaces Derived by Generalized Means and Compact Operators
Kragujevac Journal of Mathematics, Tome 41 (2017) no. 1, p. 7 .

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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.
Classification : 46A45 46B15, 46B50
Keywords: Difference operator, generalized means, $\alpha$-, $\beta$-, $\gamma$- duals, matrix transformation, compact operator, Hausdorff measure of noncompactness 
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     author = {A. Maji and A. Manna and P. D. Srivastava},
     title = {Some $B${-Difference} {Sequence} {Spaces} {Derived} by {Generalized} {Means} and {Compact} {Operators}},
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A. Maji; A. Manna; P. D. Srivastava. Some $B$-Difference Sequence Spaces Derived by Generalized Means and Compact Operators. Kragujevac Journal of Mathematics, Tome 41 (2017) no. 1, p. 7 . http://geodesic.mathdoc.fr/item/KJM_2017_41_1_a0/