{"paper":{"title":"Generalized Browder's and Weyl's Theorems for Generalized Derivations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Enrico Boasso, Mohamed Amouch","submitted_at":"2013-06-03T17:00:29Z","abstract_excerpt":"Given Banach spaces $\\X$ and $\\Y$ and Banach space operators $A\\in L(\\X)$ and $B\\in L(\\Y)$, let $\\rho\\colon L(\\Y,\\X)\\to L(\\Y,\\X)$ denote the generalized derivation defined by $A$ and $B$, i.e., $\\rho (U)=AU-UB$ ($U\\in L(\\Y,\\X)$). The main objective of this article is to study Weyl and Browder type theorems for $\\rho\\in L(L(\\Y,\\X))$. To this end, however, first the isolated points of the spectrum and the Drazin spectrum of $\\rho\\in L(L(\\Y,\\X))$ need to be characterized. In addition, it will be also proved that if $A$ and $B$ are polaroid (respectively isoloid), then $\\rho$ is polaroid (respecti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0499","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"}