{"paper":{"title":"Closure of the cone of sums of 2d-powers in real topological algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Mehdi Ghasemi, Salma Kuhlmann","submitted_at":"2011-10-13T18:00:43Z","abstract_excerpt":"Let $R$ be a unitary commutative real algebra and $K\\subseteq Hom(R,\\mathbb{R})$, closed with respect to the product topology. We consider $R$ endowed with the topology $\\mathcal{T}_K$, induced by the family of seminorms $\\rho_{\\alpha}(a):=|\\alpha(a)|$, for $\\alpha\\in K$ and $a\\in R$. In case $K$ is compact, we also consider the topology induced by $\\|a\\|_K:=\\sup_{\\alpha\\in K}|\\alpha(a)|$ for $a\\in R$. If $K$ is Zariski dense, then those topologies are Hausdorff. In this paper we prove that the closure of the cone of sums of 2d-powers, $\\sum R^{2d}$, with respect to those two topologies is equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3016","kind":"arxiv","version":3},"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"}