{"paper":{"title":"Spectra of Upper-triangular Operator Matrix","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Wu Junde, Zhang Shifang, Zhong Huaijie","submitted_at":"2009-06-27T09:25:45Z","abstract_excerpt":"Let $X$ and $Y$ be Banach spaces, $A\\in B(X)$, $B\\in B(Y)$, $C\\in B(Y, X)$, $M_{C}=({cc}A&C 0&B)$ be the operator matrix acting on the Banach space $X\\oplus Y$. In this paper, we give out 20 kind spectra structure of $M_C$, decide 18 kind spectra filling-in-hole properties of $M_C$, and present 10 examples to show that some conclusions about the spectra structure or filling-in-hole properties of $M_C$ are not true."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.5055","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"}