{"paper":{"title":"On some study of the fine spectra of generalized difference operator $\\Delta_{a,b}$ on $\\ell_p \\ (1<p<\\infty)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Arnab Patra, P. D. Srivastava, Riddhick Birbonshi","submitted_at":"2018-07-08T16:35:31Z","abstract_excerpt":"In this paper, we determine the spectrum, the point spectrum, the continuous spectrum and the residual spectrum of the generalized difference operator $\\Delta_{a,b}$ on the sequence space $\\ell_p \\ (1< p < \\infty)$ where the real sequences $a=\\{a_k\\}$ and $b=\\{b_k\\}$ are not necessarily convergent. Hence our results generalize the work given by Akhmedov and El-Shabrawy [Math. Slovaca 65~(5) (2015) 1137--1152] for the sequence space $\\ell_p (1< p <\\infty)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02849","kind":"arxiv","version":1},"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"}