{"paper":{"title":"Limit Points for Browder Spectrum of Operator Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Abdelaziz Tajmouati, Mohammed Karmouni, Safae Alaoui Chrifi","submitted_at":"2018-11-05T17:21:27Z","abstract_excerpt":"Let $A\\in \\mathcal{B}(X)$ and $B\\in \\mathcal{B}(Y)$, where $X$ and $Y$ are Banach spaces, and let $M_{C}$ be an operator acting on $X\\oplus Y$ given by $M_C=\\begin{pmatrix} A & C \\\\ 0 & B \\\\ \\end{pmatrix}$. We investigate the limit point set of the Browder spectrum of $M_{C}$. It is shown that\n  $$ acc \\sigma_{b}(M_C)\\cup W_{acc \\sigma_{b}}= acc \\sigma_{b}(A)\\cup acc \\sigma_{b}(B)$$ where $W_{acc \\sigma_{b}}$ is a subsets of $ acc\\sigma_{*}(B)\\cap acc\\sigma_{*}(A)$ and a union of certain holes in $ acc \\sigma_{b}(M_C)$. Furthermore, several sufficient conditions for $acc\\sigma_{b}(M_C)=acc\\sig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01857","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"}