{"paper":{"title":"Tensor product of left polaroid operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"B. P. Duggal, Enrico Boasso","submitted_at":"2014-01-23T11:13:49Z","abstract_excerpt":"A Banach space operator $T\\in B(X)$ is left polaroid if for each $\\lambda\\in\\hbox{iso}\\sigma_a(T)$ there is an integer $d(\\lambda)$ such that asc $(T-\\lambda)=d(\\lambda)<\\infty$ and $(T-\\lambda)^{d(\\lambda)+1}X$ is closed; $T$ is finitely left polaroid if asc $(T-\\lambda)<\\infty$, $(T-\\lambda)X$ is closed and $\\dim(T-\\lambda)^{-1}(0)<\\infty$ at each $\\lambda\\in\\hbox{iso }\\sigma_a(T)$. The left polaroid property transfers from $A$ and $B$ to their tensor product $A\\otimes B$, hence also from $A$ and $B^*$ to the left-right multiplication operator $\\tau_{AB}$, for Hilbert space operators; an add"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5939","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"}