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arXiv · 1308.2667

Some Paranormed Difference Sequence Spaces of Order $m$ Derived by Generalized Means and Compact Operators

Amit Maji·P. D. Srivastava
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Abstract

We have introduced a new sequence space $l(r, s, t, p ;\Delta^{(m)})$ combining by using generalized means and difference operator of order $m$. We have shown that the space $l(r, s, t, p ;\Delta^{(m)})$ is complete under some suitable paranorm and it has Schauder basis. Furthermore, the $\alpha$-, $\beta$-, $\gamma$- duals of this space is computed and also obtained necessary and sufficient conditions for some matrix transformations from $l(r, s, t, p; \Delta^{(m)})$ to $l_{\infty}, l_1$. Finally, we obtained some identities or estimates for the operator norms and the Hausdorff measure of noncompactness of some matrix operators on the BK space $l_{p}(r, s, t ;\Delta^{(m)})$ by applying the Hausdorff measure of noncompactness.

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Amit Maji, P. D. Srivastava. 2013-08-10. Some Paranormed Difference Sequence Spaces of Order $m$ Derived by Generalized Means and Compact Operators. https://arxiv.org/abs/1308.2667

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