{"paper":{"title":"Some spectral properties for generalized derivations","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Farida Lombarkia, Mohamed Amouch","submitted_at":"2014-09-18T21:14:30Z","abstract_excerpt":"Given Banach spaces $\\mathcal{X}$ and $\\mathcal{Y}$ and Banach space operators $A\\in L(\\mathcal{X})$ and $B\\in L(\\mathcal{Y}).$ The generalized derivation $\\delta_{A,B} \\in L(L(\\mathcal{Y},\\mathcal{X}))$ is defined by $\\delta_{A,B}(X)=(L_{A}-R_{B})(X)=AX-XB$. This paper is concerned with the problem of the transferring the left polaroid property, from operators $A$ and $B^{*}$ to the generalized derivation $\\delta_{A,B}$. As a consequence, we give necessary and sufficient conditions for $\\delta_{A,B}$ to satisfy generalized a-Browder's theorem and generalized a-Weyl's theorem. As application, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5463","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"}