{"paper":{"title":"Upper bounds for continuous seminorms and special properties of bilinear maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Helge Glockner","submitted_at":"2011-12-08T13:04:19Z","abstract_excerpt":"If E is a locally convex topological vector space, let P(E) be the pre-ordered set of all continuous seminorms on E. We study, on the one hand, for g an infinite cardinal those locally convex spaces E which have the g-neighbourhood property in the sense of E. Jorda, i.e., spaces in which all sets M of continuous seminorms of cardinality up to g have an upper bound in P(E). On the other hand, we study bilinear maps b from a product of locally convex spaces E_1 and E_2 to a locally convex space F, which admit \"product estimates\" in the sense that for all p_{i,j} in P(F), i,j=1,2,..., there exist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1824","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"}