{"paper":{"title":"The Drazin spectrum of tensor product of Banach algebra elements and elementary operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Enrico Boasso","submitted_at":"2014-04-11T14:36:37Z","abstract_excerpt":"Given unital Banach algebras $A$ and $B$ and elements $a\\in A$ and $b\\in B$, the Drazin spectrun of $a\\otimes b\\in A\\overline{\\otimes} B$ will be fully characterized, where $A\\overline{\\otimes} B$ is a Banach algebra that is the completion of $A\\otimes B$ with respect to a uniform crossnorm. To this end, however, first the isolated points of the spectrum of $a\\otimes b\\in A\\overline{\\otimes} B$ need to be characterized. On the other hand, given Banach spaces $X$ and $Y$ and Banach space operators $S\\in L(X)$ and $T\\in L(Y)$, using similar arguments the Drazin spectrum of $\\tau_{ST}\\in L(L(Y,X)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3121","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"}