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Some $B$-Difference Sequence Spaces Derived by Using Generalized Means and Compact Operators | | Amit Maji
; Atanu Manna
; P. D. Srivastava
; | | Date: |
19 Jul 2013 | | Abstract: | 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 $X(r, s, t, p ; B)$ for $X in {c(p), c_0(p), l(p)}$
have Schauder basis. Furthermore, the $alpha$-, $eta$-, $gamma$- 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. | | Source: | arXiv, 1307.5817 | | Services: | Forum | Review | PDF | Favorites | |
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