{"paper":{"title":"Ideal structures in vector-valued polynomial spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"\\'Angeles Prieto, Silvia Lassalle, Ver\\'onica Dimant","submitted_at":"2015-12-29T18:10:41Z","abstract_excerpt":"This paper is concerned with the study of geometric structures in spaces of polynomials. More precisely, we discuss for $E$ and $F$ Banach spaces, whether the class of weakly continuous on bounded sets $n$-homogeneous polynomials, $\\mathcal P_w(^n E, F)$, is an HB-subspace or an $M(1,C)$-ideal in the space of continuous $n$-homogeneous polynomials, $\\mathcal P(^n E, F)$. We establish sufficient conditions under which the problem can be positively solved. Some examples are given. We also study when some ideal structures pass from $\\mathcal P_w(^n E, F)$ as an ideal in $\\mathcal P(^n E, F)$ to t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08741","kind":"arxiv","version":2},"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"}