{"paper":{"title":"Some Paranormed Difference Sequence Spaces of Order $m$ Derived by Generalized Means and Compact Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Amit Maji, P. D. Srivastava","submitted_at":"2013-08-10T15:28:01Z","abstract_excerpt":"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 non"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2667","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}