{"paper":{"title":"Compact perturbations and consequent hereditarily polaroid operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"B. P. Duggal","submitted_at":"2015-11-04T17:35:52Z","abstract_excerpt":"A Banach space operator $A\\in B({\\cal{X}})$ is polaroid, $A\\in {\\cal{P}}$, if the isolated points of the spectrum $\\sigma(A)$ are poles of the operator; $A$ is hereditarily polaroid, $A\\in{\\cal{HP}}$, if every restriction of $A$ to a closed invariant subspace is polaroid. Operators $A\\in{\\cal{HP}}$ have SVEP on $\\Phi_{sf}(A)=\\{\\lambda: A-\\lambda$ is semi Fredholm $\\}$: This, in answer to a question posed by Li and Zhou (Studia Math. 221(2014), 175-192), proves the necessity of the condition $\\Phi_{sf}^+(A)=\\emptyset$. A sufficient condition for $A\\in B({\\cal{X}})$ to have SVEP on $\\Phi_{sf}(A)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01408","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"}