{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NKFTNMO4CKQCDJAVIWCHGVVIDK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a454236b5b558df6a1355c3d9565a1f4af5e8e9f087c447fd5006012b1117e5b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.SP","submitted_at":"2014-09-18T21:14:30Z","title_canon_sha256":"e5f78e1858c008e795791fd491a8a4dea9914eecbae23ea017119464063e9e62"},"schema_version":"1.0","source":{"id":"1409.5463","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.5463","created_at":"2026-05-18T02:42:27Z"},{"alias_kind":"arxiv_version","alias_value":"1409.5463v1","created_at":"2026-05-18T02:42:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.5463","created_at":"2026-05-18T02:42:27Z"},{"alias_kind":"pith_short_12","alias_value":"NKFTNMO4CKQC","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NKFTNMO4CKQCDJAV","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NKFTNMO4","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:cdff40877544db1f3d126fc82a3f2671ce36c8cfc0f6925630a334a228732086","target":"graph","created_at":"2026-05-18T02:42:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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, ","authors_text":"Farida Lombarkia, Mohamed Amouch","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.SP","submitted_at":"2014-09-18T21:14:30Z","title":"Some spectral properties for generalized derivations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5463","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2f55eb37bd88f2c91b67d12558a013efe733cd171ba1c9919d7af4ef4c909a2d","target":"record","created_at":"2026-05-18T02:42:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a454236b5b558df6a1355c3d9565a1f4af5e8e9f087c447fd5006012b1117e5b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.SP","submitted_at":"2014-09-18T21:14:30Z","title_canon_sha256":"e5f78e1858c008e795791fd491a8a4dea9914eecbae23ea017119464063e9e62"},"schema_version":"1.0","source":{"id":"1409.5463","kind":"arxiv","version":1}},"canonical_sha256":"6a8b36b1dc12a021a41545847356a81abcad4029752bfc87222a003e4a8c6cd7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a8b36b1dc12a021a41545847356a81abcad4029752bfc87222a003e4a8c6cd7","first_computed_at":"2026-05-18T02:42:27.526625Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:27.526625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nmm6QO4Y4F/SfvD2WIeavlLiQLGjEuCbClJntPF+jAgzRbc+h5XQUel0eWIRmtZBKf0ObD5vvXatblEusacnBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:27.527517Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.5463","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f55eb37bd88f2c91b67d12558a013efe733cd171ba1c9919d7af4ef4c909a2d","sha256:cdff40877544db1f3d126fc82a3f2671ce36c8cfc0f6925630a334a228732086"],"state_sha256":"385fc9dbd61f6dffd0eef1bff57c3b5c1e4dbebd8e156b551154fbeac18e7a19"}